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Simplifying 8x(x + -7) = (2x + 9)(x + -7) Reorder the terms: 8x(-7 + x) = (2x + 9)(x + -7) (-7 * 8x + x * 8x) = (2x + 9)(x + -7) (-56x + 8x2) = (2x + 9)(x + -7) Reorder the terms: -56x + 8x2 = (9 + 2x)(x + -7) Reorder the terms: -56x + 8x2 = (9 + 2x)(-7 + x) Multiply (9 + 2x) * (-7 + x) -56x + 8x2 = (9(-7 + x) + 2x * (-7 + x)) -56x + 8x2 = ((-7 * 9 + x * 9) + 2x * (-7 + x)) -56x + 8x2 = ((-63 + 9x) + 2x * (-7 + x)) -56x + 8x2 = (-63 + 9x + (-7 * 2x + x * 2x)) -56x + 8x2 = (-63 + 9x + (-14x + 2x2)) Combine like terms: 9x + -14x = -5x -56x + 8x2 = (-63 + -5x + 2x2) Solving -56x + 8x2 = -63 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: 63 + -56x + 5x + 8x2 + -2x2 = -63 + -5x + 2x2 + 63 + 5x + -2x2 Combine like terms: -56x + 5x = -51x 63 + -51x + 8x2 + -2x2 = -63 + -5x + 2x2 + 63 + 5x + -2x2 Combine like terms: 8x2 + -2x2 = 6x2 63 + -51x + 6x2 = -63 + -5x + 2x2 + 63 + 5x + -2x2 Reorder the terms: 63 + -51x + 6x2 = -63 + 63 + -5x + 5x + 2x2 + -2x2 Combine like terms: -63 + 63 = 0 63 + -51x + 6x2 = 0 + -5x + 5x + 2x2 + -2x2 63 + -51x + 6x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 63 + -51x + 6x2 = 0 + 2x2 + -2x2 63 + -51x + 6x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 63 + -51x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(21 + -17x + 2x2) = 0 Factor a trinomial. 3((3 + -2x)(7 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1.5, 7}
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