Which value for the constant d makes x=-3 an extraneous solution in the following equation? \sqrt{25+3x}=d+2x

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Which value for the constant d makes x=-3  an extraneous solution in the following equation? \sqrt{25+3x}=d+2x

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Given Equation and Goal: We are given the equation √(25+3x) = d+2x and we want to find the value of d that makes x=-3 an extraneous solution. An extraneous solution is a solution that is derived from an algebraic manipulation but is not a solution to the original equation. To find the value of d, we will first substitute x=-3 into the equation and solve for d.Substitute x = -3: Substitute x = -3 into the equation √(25+3x) = d+2x. √(25+3(-3)) = d+2(-3) √(25-9) = d-6 √16 = d-6Simplify Square Root: Simplify the square root of 16. 4 = d-6Add 6 to Solve: Add 6 to both sides of the equation to solve for d. 4 + 6 = d 10 = dCheck for Extraneous Solution: We have found that d = 10. However, we need to check if x = -3 is indeed an extraneous solution. To do this, we substitute x = -3 back into the original equation and see if the equation is valid or leads to a contradiction.Substitute x = -3 Again: Substitute x = -3 into the original equation with d = 10. √(25+3(-3)) = 10+2(-3) √(25-9) = 10-6 √16 = 4 4 = 4 This is a true statement, which means that x = -3 is not an extraneous solution for d = 10. This contradicts our goal of finding a d that makes x = -3 an extraneous solution. Therefore, we have made a math error in our reasoning.

Which value for the constant $d$ makes $x=-3$ an extraneous solution in the following equation? $\sqrt{25+3x}=d+2x$

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Which value for the constant ddd makes x=−3x=-3x=−3 an extraneous solution in the following equation? 25+3x=d+2x\sqrt{25+3x}=d+2x25+3x​=d+2x

Which value for the constant $d$ makes $x=-3$ an extraneous solution in the following equation? $\sqrt{25+3x}=d+2x$