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Simplifying (2x + -3)(2x + -3) = 16 Reorder the terms: (-3 + 2x)(2x + -3) = 16 Reorder the terms: (-3 + 2x)(-3 + 2x) = 16 Multiply (-3 + 2x) * (-3 + 2x) (-3(-3 + 2x) + 2x * (-3 + 2x)) = 16 ((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 16 ((9 + -6x) + 2x * (-3 + 2x)) = 16 (9 + -6x + (-3 * 2x + 2x * 2x)) = 16 (9 + -6x + (-6x + 4x2)) = 16 Combine like terms: -6x + -6x = -12x (9 + -12x + 4x2) = 16 Solving 9 + -12x + 4x2 = 16 Solving for variable 'x'. Reorder the terms: 9 + -16 + -12x + 4x2 = 16 + -16 Combine like terms: 9 + -16 = -7 -7 + -12x + 4x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -7 + -12x + 4x2 = 0 Factor a trinomial. (-1 + -2x)(7 + -2x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5Solution
x = {-0.5, 3.5}
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