√4x = x - 3What are all values of x that satisfy the given equation?I. 1II. 9

Explanation

Choice B is correct. Squaring both sides of the equation √4x = x − 3 yields 4x = (x − 3)2 , or 4x = (x − 3)(x − 3). Applying the distributive property on the right-hand side of the equation 4x = (x − 3)(x − 3) yields 4x = x2 − 3x − 3x + 9. Subtracting 4x from both sides of 4x = x2 − 3x − 3x + 9 yields 0 = x2 − 3x − 3x − 4x + 9, which can be rewritten as 0 = x2 − 10x + 9. Factoring the right-hand side of 0 = x2 −10x + 9 gives 0 = (x − 1)(x − 9). By the zero product property, if 0 = (x − 1)(x − 9), then 0 = x − 1 or 0 = x − 9. Adding 1 to both sides of 0 = x − 1 gives x = 1. Adding 9 to both sides of 0 = x − 9 gives x = 9. Substituting these values for x into the given equation will determine whether they satisfy the equation. Substituting 1 for x in the given equation yields √4(1) = 1 − 3, or √4 = -2, which is false. Therefore, x = 1 doesn't satisfy the given equation. Substituting 9 for x in the given equation yields √4(9) = 9-3 or √36 = 6, which is true. Therefore, x = 9 satisfies the given equation.