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Simplifying -2(x + -5)(x + -5) = (2x + 1)(2x + 1) + -57 Reorder the terms: -2(-5 + x)(x + -5) = (2x + 1)(2x + 1) + -57 Reorder the terms: -2(-5 + x)(-5 + x) = (2x + 1)(2x + 1) + -57 Multiply (-5 + x) * (-5 + x) -2(-5(-5 + x) + x(-5 + x)) = (2x + 1)(2x + 1) + -57 -2((-5 * -5 + x * -5) + x(-5 + x)) = (2x + 1)(2x + 1) + -57 -2((25 + -5x) + x(-5 + x)) = (2x + 1)(2x + 1) + -57 -2(25 + -5x + (-5 * x + x * x)) = (2x + 1)(2x + 1) + -57 -2(25 + -5x + (-5x + x2)) = (2x + 1)(2x + 1) + -57 Combine like terms: -5x + -5x = -10x -2(25 + -10x + x2) = (2x + 1)(2x + 1) + -57 (25 * -2 + -10x * -2 + x2 * -2) = (2x + 1)(2x + 1) + -57 (-50 + 20x + -2x2) = (2x + 1)(2x + 1) + -57 Reorder the terms: -50 + 20x + -2x2 = (1 + 2x)(2x + 1) + -57 Reorder the terms: -50 + 20x + -2x2 = (1 + 2x)(1 + 2x) + -57 Multiply (1 + 2x) * (1 + 2x) -50 + 20x + -2x2 = (1(1 + 2x) + 2x * (1 + 2x)) + -57 -50 + 20x + -2x2 = ((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -57 -50 + 20x + -2x2 = ((1 + 2x) + 2x * (1 + 2x)) + -57 -50 + 20x + -2x2 = (1 + 2x + (1 * 2x + 2x * 2x)) + -57 -50 + 20x + -2x2 = (1 + 2x + (2x + 4x2)) + -57 Combine like terms: 2x + 2x = 4x -50 + 20x + -2x2 = (1 + 4x + 4x2) + -57 Reorder the terms: -50 + 20x + -2x2 = 1 + -57 + 4x + 4x2 Combine like terms: 1 + -57 = -56 -50 + 20x + -2x2 = -56 + 4x + 4x2 Solving -50 + 20x + -2x2 = -56 + 4x + 4x2 Solving for variable 'x'. Reorder the terms: -50 + 56 + 20x + -4x + -2x2 + -4x2 = -56 + 4x + 4x2 + 56 + -4x + -4x2 Combine like terms: -50 + 56 = 6 6 + 20x + -4x + -2x2 + -4x2 = -56 + 4x + 4x2 + 56 + -4x + -4x2 Combine like terms: 20x + -4x = 16x 6 + 16x + -2x2 + -4x2 = -56 + 4x + 4x2 + 56 + -4x + -4x2 Combine like terms: -2x2 + -4x2 = -6x2 6 + 16x + -6x2 = -56 + 4x + 4x2 + 56 + -4x + -4x2 Reorder the terms: 6 + 16x + -6x2 = -56 + 56 + 4x + -4x + 4x2 + -4x2 Combine like terms: -56 + 56 = 0 6 + 16x + -6x2 = 0 + 4x + -4x + 4x2 + -4x2 6 + 16x + -6x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 6 + 16x + -6x2 = 0 + 4x2 + -4x2 6 + 16x + -6x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 6 + 16x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 8x + -3x2) = 0 Factor a trinomial. 2((3 + -1x)(1 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {3, -0.3333333333}
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