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Simplifying (2x + -3)(2x + 3) + -2(x + -1) = 5 Reorder the terms: (-3 + 2x)(2x + 3) + -2(x + -1) = 5 Reorder the terms: (-3 + 2x)(3 + 2x) + -2(x + -1) = 5 Multiply (-3 + 2x) * (3 + 2x) (-3(3 + 2x) + 2x * (3 + 2x)) + -2(x + -1) = 5 ((3 * -3 + 2x * -3) + 2x * (3 + 2x)) + -2(x + -1) = 5 ((-9 + -6x) + 2x * (3 + 2x)) + -2(x + -1) = 5 (-9 + -6x + (3 * 2x + 2x * 2x)) + -2(x + -1) = 5 (-9 + -6x + (6x + 4x2)) + -2(x + -1) = 5 Combine like terms: -6x + 6x = 0 (-9 + 0 + 4x2) + -2(x + -1) = 5 (-9 + 4x2) + -2(x + -1) = 5 Reorder the terms: -9 + 4x2 + -2(-1 + x) = 5 -9 + 4x2 + (-1 * -2 + x * -2) = 5 -9 + 4x2 + (2 + -2x) = 5 Reorder the terms: -9 + 2 + -2x + 4x2 = 5 Combine like terms: -9 + 2 = -7 -7 + -2x + 4x2 = 5 Solving -7 + -2x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: -7 + -5 + -2x + 4x2 = 5 + -5 Combine like terms: -7 + -5 = -12 -12 + -2x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -12 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -1x + 2x2) = 0 Factor a trinomial. 2((-3 + -2x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1.5, 2}
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