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Simplifying (2x + 1)(2x + 1) + -8(2x + 1) = -15 Reorder the terms: (1 + 2x)(2x + 1) + -8(2x + 1) = -15 Reorder the terms: (1 + 2x)(1 + 2x) + -8(2x + 1) = -15 Multiply (1 + 2x) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x)) + -8(2x + 1) = -15 ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -8(2x + 1) = -15 ((1 + 2x) + 2x * (1 + 2x)) + -8(2x + 1) = -15 (1 + 2x + (1 * 2x + 2x * 2x)) + -8(2x + 1) = -15 (1 + 2x + (2x + 4x2)) + -8(2x + 1) = -15 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2) + -8(2x + 1) = -15 Reorder the terms: 1 + 4x + 4x2 + -8(1 + 2x) = -15 1 + 4x + 4x2 + (1 * -8 + 2x * -8) = -15 1 + 4x + 4x2 + (-8 + -16x) = -15 Reorder the terms: 1 + -8 + 4x + -16x + 4x2 = -15 Combine like terms: 1 + -8 = -7 -7 + 4x + -16x + 4x2 = -15 Combine like terms: 4x + -16x = -12x -7 + -12x + 4x2 = -15 Solving -7 + -12x + 4x2 = -15 Solving for variable 'x'. Reorder the terms: -7 + 15 + -12x + 4x2 = -15 + 15 Combine like terms: -7 + 15 = 8 8 + -12x + 4x2 = -15 + 15 Combine like terms: -15 + 15 = 0 8 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -3x + x2) = 0 Factor a trinomial. 4((1 + -1x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 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, 2}
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