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Simplifying (2x)(2x) = (2x + 4)(2x + 4) + -1(x + 1)(x + 1) Remove parenthesis around (2x) 2x(2x) = (2x + 4)(2x + 4) + -1(x + 1)(x + 1) Remove parenthesis around (2x) 2x * 2x = (2x + 4)(2x + 4) + -1(x + 1)(x + 1) Reorder the terms for easier multiplication: 2 * 2x * x = (2x + 4)(2x + 4) + -1(x + 1)(x + 1) Multiply 2 * 2 4x * x = (2x + 4)(2x + 4) + -1(x + 1)(x + 1) Multiply x * x 4x2 = (2x + 4)(2x + 4) + -1(x + 1)(x + 1) Reorder the terms: 4x2 = (4 + 2x)(2x + 4) + -1(x + 1)(x + 1) Reorder the terms: 4x2 = (4 + 2x)(4 + 2x) + -1(x + 1)(x + 1) Multiply (4 + 2x) * (4 + 2x) 4x2 = (4(4 + 2x) + 2x * (4 + 2x)) + -1(x + 1)(x + 1) 4x2 = ((4 * 4 + 2x * 4) + 2x * (4 + 2x)) + -1(x + 1)(x + 1) 4x2 = ((16 + 8x) + 2x * (4 + 2x)) + -1(x + 1)(x + 1) 4x2 = (16 + 8x + (4 * 2x + 2x * 2x)) + -1(x + 1)(x + 1) 4x2 = (16 + 8x + (8x + 4x2)) + -1(x + 1)(x + 1) Combine like terms: 8x + 8x = 16x 4x2 = (16 + 16x + 4x2) + -1(x + 1)(x + 1) Reorder the terms: 4x2 = 16 + 16x + 4x2 + -1(1 + x)(x + 1) Reorder the terms: 4x2 = 16 + 16x + 4x2 + -1(1 + x)(1 + x) Multiply (1 + x) * (1 + x) 4x2 = 16 + 16x + 4x2 + -1(1(1 + x) + x(1 + x)) 4x2 = 16 + 16x + 4x2 + -1((1 * 1 + x * 1) + x(1 + x)) 4x2 = 16 + 16x + 4x2 + -1((1 + 1x) + x(1 + x)) 4x2 = 16 + 16x + 4x2 + -1(1 + 1x + (1 * x + x * x)) 4x2 = 16 + 16x + 4x2 + -1(1 + 1x + (1x + x2)) Combine like terms: 1x + 1x = 2x 4x2 = 16 + 16x + 4x2 + -1(1 + 2x + x2) 4x2 = 16 + 16x + 4x2 + (1 * -1 + 2x * -1 + x2 * -1) 4x2 = 16 + 16x + 4x2 + (-1 + -2x + -1x2) Reorder the terms: 4x2 = 16 + -1 + 16x + -2x + 4x2 + -1x2 Combine like terms: 16 + -1 = 15 4x2 = 15 + 16x + -2x + 4x2 + -1x2 Combine like terms: 16x + -2x = 14x 4x2 = 15 + 14x + 4x2 + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 4x2 = 15 + 14x + 3x2 Solving 4x2 = 15 + 14x + 3x2 Solving for variable 'x'. Reorder the terms: -15 + -14x + 4x2 + -3x2 = 15 + 14x + 3x2 + -15 + -14x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -15 + -14x + 1x2 = 15 + 14x + 3x2 + -15 + -14x + -3x2 Reorder the terms: -15 + -14x + 1x2 = 15 + -15 + 14x + -14x + 3x2 + -3x2 Combine like terms: 15 + -15 = 0 -15 + -14x + 1x2 = 0 + 14x + -14x + 3x2 + -3x2 -15 + -14x + 1x2 = 14x + -14x + 3x2 + -3x2 Combine like terms: 14x + -14x = 0 -15 + -14x + 1x2 = 0 + 3x2 + -3x2 -15 + -14x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -15 + -14x + 1x2 = 0 Factor a trinomial. (-1 + -1x)(15 + -1x) = 0Subproblem 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 '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15Solution
x = {-1, 15}
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