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what are all the solutions to the equation above so we have 4x squared is equal to 52 well if we want to solve for X we can just divide both sides by 4 and then we get x squared is equal to 52 divided by 4 is 13 so X could be equal to if x squared is equal to 13 that that means X could be the positive or the negative square root of 13 so X is going to be equal to the positive or negative square root of 13 and you could check your answer take positive 13 if you if you take or take the take positive square root of 13 well if you square it you're gonna get 13 and then multiply it times 4 you're gonna get 52 take the negative square root of 13 well when you square it you're going to get 13 because the negative times a negative is positive and then you multiply times 4 you're gonna get 52 so X could be negative square root of 13 oh and or or X could be X could be or the two solutions are X is the negative square root of 13 and X is equal to the positive square root of 13 so that's our choice all right over there