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MIAMI — Ben Carson, the retired pediatric neurosurgeon who ended his presidential bid last week, plans to endorse Donald J. Trump on Friday morning, three people familiar with the discussions said.

Mr. Carson will make his endorsement, first reported by The Washington Post, at a morning press conference with Mr. Trump at Mar-a-Lago, his private club in Palm Beach, Fla.

In an interview with John Gibson on Fox News Radio, Mr. Carson said that there was more to Mr. Trump than meets the eye.

“There’s the Donald Trump that you see on television and who gets out in front of big audiences, and there’s the Donald Trump behind the scenes,” Mr. Carson said. “They’re not the same person.”

“One’s very much an entertainer, and one is actually a thinking individual,” he said.

Mr. Carson said that Mr. Trump would be “a lot better than Hillary” and that he would not be as bad as many conservatives fear. He said that Mr. Trump was “more reasonable” than people realized and that he could be an asset to Republican efforts to maintain control of Congress because he is harnessing the anger of the American public.

During Mr. Carson’s run, Mr. Trump compared him to a child molester, called him “super low energy” and questioned his religion when they were competing against each other for the Republican presidential nomination.

But Mr. Carson had frayed relations with Mr. Trump’s main rival, Senator Ted Cruz. Mr. Carson blamed the Cruz campaign for spreading false information on the day of the Iowa caucuses that he was pulling out of the race, for which Mr. Cruz later apologized.

While endorsements typically don’t sway many voters, Mr. Carson continues to have a devoted base of support, particularly among evangelicals, whom Mr. Trump and Mr. Cruz have been courting.