Hillary Clinton and Donald Trump have emerged from party conventions needing to expand their base of support as they compete in the race for the White House, several political scientists agreed.

Trump, whose base remains mostly blue-collar white voters, surprised many in his nomination acceptance speech at the Republican National Convention when he called for protection of rights for “wonderful” transgender people and gays, said he loved Muslims and Latinos and promised other measures that bucked decades of Republican orthodoxy — such as opposing trade agreements — to broaden his appeal.

In Clinton’s speech at the Democratic National Convention, she made direct appeals to independents, undecided voters and disgruntled Republicans, backing it up with surrogates who were independents, Republicans and top military leaders. Clinton is seeking to expand her base beyond African-Americans, Latinos, and college-educated and centrist white Democrats.

Political scientists have said each candidate’s historically high unfavorable ratings inside and outside their parties will hamper significant growth in support. And if the candidates fail to expand their base of support, experts warn, a contest between two polarizing candidates will lead to a race mired deeper in mud than ever, and yield a president for an even more deeply divided nation.

“There is no question this is an extremely unusual election,” said Professor Stanley Feldman of Stony Brook University.

“In the middle,” said Professor Brooks D. Simpson of Arizona State University, “are voters who are trying to figure out whether they will cast their ballot for the devil they know as opposed to the devil they don’t. They are still trying to figure out whether Trump is worse, and whether he’s fundamentally unstable and untrustworthy — a man who will make decisions that will prove disastrous. Clinton promises more of the same . . . she won’t revolutionize anything, but she’s unlikely to break all the toys.”

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At the Democratic convention in Philadelphia, Clinton was preceded by speakers that included former New York City Mayor Michael Bloomberg, an independent; Doug Elmets, a former aide to President Ronald Reagan; and retired Marine Gen. John Allen, who commanded troops in Afghanistan.

“You heard from Republicans and independents,” Clinton said in her acceptance speech Thursday night. “I will be a president for Democrats, Republicans, independents . . . for all those who vote for me and for those who don’t. For all Americans, together.”

The party provided a rare speaking slot to a non-Democrat when Bloomberg made a powerful pitch for Clinton — “a problem-solver, not a bomb-thrower” — to “my fellow independents.”

“I know what it’s like to have neither party completely represent my views or values,” Bloomberg said. “Whatever our disagreements may be, I’ve come here to say we must put them aside for the good of our country and we must unite around the candidate who can defeat a dangerous demagogue.”

“I am a Republican,” said Elmets of California, a member of the Republican Reagan administration who was given a prime speaking spot Thursday. “I am here tonight to say I knew Ronald Reagan, I worked for Ronald Reagan. Donald Trump, you are no Ronald Reagan.”

Clinton later ticked off several concerns, including job growth and reducing college loan debt, that cross party lines and said: “Whatever party you belong to, or if you belong to no party at all . . . this is your campaign.”

She and President Barack Obama also made several direct overtures to the ardent supporters of Clinton’s rival in the primaries, Vermont Sen. Bernie Sanders, and his policies, including a $15 minimum wage. Sanders had captivated the liberal, mostly young wing of the party, some of whom were still protesting during Thursday night’s final convention session.

The night before, Obama urged all delegates “to be as vocal and as organized and as persistent as Bernie Sanders supporters have been.”

“That’s right, ‘Feel the Bern,’ ” Obama said.

Superdelegate Stephanie Miner, the mayor of Syracuse, said heartfelt discussions were underway all week between leaders and rank-and-file supporters to unite the party.

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“From my experience, it’s definitely happening,” Miner said in an interview from Philadelphia. She said the key was an argument from Sanders, which she paraphrased: “It’s easy to boo. What are you going to do when your children wake up in a Donald Trump world?”

In Cleveland, Trump in his nomination acceptance a week before also worked to expand his base.

“My sole and exclusive mission is to go to work for our country — to go to work for you,” Trump said, repeating that he is the “voice” for all Americans.

Trump moved to broaden his appeal by supporting a $10 federal minimum wage. Previously, the businessman said the federal rate was too high at $7.25 an hour. Trump also had Silicon Valley billionaire Peter Thiel make the first speech by an openly gay man at a Republican convention and called for protection of the rights of transgender people and gays.

He called for scrapping long-established trade policies backed by the threat of high tariffs to force American companies to pull overseas operations and investments back to the United States as part of his appeal to working-class Americans whom he said lost jobs to bad trade deals.

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His millennial daughter, Ivanka, in a key role introducing her father before his acceptance speech, called for equal pay for women doing the same jobs as men and for affordable day care.

A Republican delegate, Assembly GOP leader Brian Kolb of Canandaigua, said Republicans are coming together for Trump since the convention: “You may not agree with everything Donald Trump says, but when it comes to Donald Trump, who is willing to take on the status quo, and Hillary Clinton, who is the status quo, Republicans I talk to — and not just those in elected office — say the more you crystallize what the choice is, there is no way they are voting for Hillary.”

Kerry Haynie, a political scientist at Duke University, said Trump needs to back off on name-calling and start appealing to more voters through new policies and details to the policies he’s already promised.

“The general strategy is that you have to carefully run to your base in the primary and then very quickly pivot so you can run to the center,” Haynie said. “Trump did an amazingly good job of appealing to the Republican primary electorate. But that’s not enough to get him elected . . . .”

Meena Bose, political science professor at Hofstra University and director of the Peter S. Kalikow Center for the Study of the American Presidency, said Trump could attract more voters if he provides details to his broad exhortations to create jobs and defeat terrorism. “The more specifics that are provided are best for the independents,” Bose said.

Clinton must create a “kind of spirit and activism” to attract mostly young liberals who flocked to Sanders and his call to overhaul the political and economic systems, said Morris P. Fiorina, a political scientist at Stanford University.

“Hillary has to provide a sense that she has a true change of heart, which she hasn’t; and Trump has to show he is legitimate, and he hasn’t,” Fiorina said.

A divisive primary and polarized conventions may lead to an especially nasty general campaign, the experts said.

“It’s just going to be ugly, just a down-in-the-dirt campaign,” Fiorina said. “All they can do is drive each other’s negatives down . . . Trump is the one thing that motivates Democrats and Hillary is the one thing that motivates Republicans — even more so.”