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Simplifying (2x + 7)(7 + -2x) = 49 + x(x + 2) Reorder the terms: (7 + 2x)(7 + -2x) = 49 + x(x + 2) Multiply (7 + 2x) * (7 + -2x) (7(7 + -2x) + 2x * (7 + -2x)) = 49 + x(x + 2) ((7 * 7 + -2x * 7) + 2x * (7 + -2x)) = 49 + x(x + 2) ((49 + -14x) + 2x * (7 + -2x)) = 49 + x(x + 2) (49 + -14x + (7 * 2x + -2x * 2x)) = 49 + x(x + 2) (49 + -14x + (14x + -4x2)) = 49 + x(x + 2) Combine like terms: -14x + 14x = 0 (49 + 0 + -4x2) = 49 + x(x + 2) (49 + -4x2) = 49 + x(x + 2) Reorder the terms: 49 + -4x2 = 49 + x(2 + x) 49 + -4x2 = 49 + (2 * x + x * x) 49 + -4x2 = 49 + (2x + x2) Add '-49' to each side of the equation. 49 + -49 + -4x2 = 49 + 2x + -49 + x2 Combine like terms: 49 + -49 = 0 0 + -4x2 = 49 + 2x + -49 + x2 -4x2 = 49 + 2x + -49 + x2 Reorder the terms: -4x2 = 49 + -49 + 2x + x2 Combine like terms: 49 + -49 = 0 -4x2 = 0 + 2x + x2 -4x2 = 2x + x2 Solving -4x2 = 2x + x2 Solving for variable 'x'. Reorder the terms: -2x + -4x2 + -1x2 = 2x + x2 + -2x + -1x2 Combine like terms: -4x2 + -1x2 = -5x2 -2x + -5x2 = 2x + x2 + -2x + -1x2 Reorder the terms: -2x + -5x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -2x + -5x2 = 0 + x2 + -1x2 -2x + -5x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(2 + 5x) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4Solution
x = {0, -0.4}
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