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Simplifying x2 + 6x + -16 = 2x2 + 7x + -1(x2 + -9) Reorder the terms: -16 + 6x + x2 = 2x2 + 7x + -1(x2 + -9) Reorder the terms: -16 + 6x + x2 = 2x2 + 7x + -1(-9 + x2) -16 + 6x + x2 = 2x2 + 7x + (-9 * -1 + x2 * -1) -16 + 6x + x2 = 2x2 + 7x + (9 + -1x2) Reorder the terms: -16 + 6x + x2 = 9 + 7x + 2x2 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -16 + 6x + x2 = 9 + 7x + 1x2 Solving -16 + 6x + x2 = 9 + 7x + 1x2 Solving for variable 'x'. Reorder the terms: -16 + -9 + 6x + -7x + x2 + -1x2 = 9 + 7x + 1x2 + -9 + -7x + -1x2 Combine like terms: -16 + -9 = -25 -25 + 6x + -7x + x2 + -1x2 = 9 + 7x + 1x2 + -9 + -7x + -1x2 Combine like terms: 6x + -7x = -1x -25 + -1x + x2 + -1x2 = 9 + 7x + 1x2 + -9 + -7x + -1x2 Combine like terms: x2 + -1x2 = 0 -25 + -1x + 0 = 9 + 7x + 1x2 + -9 + -7x + -1x2 -25 + -1x = 9 + 7x + 1x2 + -9 + -7x + -1x2 Reorder the terms: -25 + -1x = 9 + -9 + 7x + -7x + 1x2 + -1x2 Combine like terms: 9 + -9 = 0 -25 + -1x = 0 + 7x + -7x + 1x2 + -1x2 -25 + -1x = 7x + -7x + 1x2 + -1x2 Combine like terms: 7x + -7x = 0 -25 + -1x = 0 + 1x2 + -1x2 -25 + -1x = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -25 + -1x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + x)' equal to zero and attempt to solve: Simplifying 25 + x = 0 Solving 25 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + x = 0 + -25 x = 0 + -25 Combine like terms: 0 + -25 = -25 x = -25 Simplifying x = -25Solution
x = {-25}
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