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Simplifying 8(x2 + -6x + 9) = 7(x2 + -9) Reorder the terms: 8(9 + -6x + x2) = 7(x2 + -9) (9 * 8 + -6x * 8 + x2 * 8) = 7(x2 + -9) (72 + -48x + 8x2) = 7(x2 + -9) Reorder the terms: 72 + -48x + 8x2 = 7(-9 + x2) 72 + -48x + 8x2 = (-9 * 7 + x2 * 7) 72 + -48x + 8x2 = (-63 + 7x2) Solving 72 + -48x + 8x2 = -63 + 7x2 Solving for variable 'x'. Reorder the terms: 72 + 63 + -48x + 8x2 + -7x2 = -63 + 7x2 + 63 + -7x2 Combine like terms: 72 + 63 = 135 135 + -48x + 8x2 + -7x2 = -63 + 7x2 + 63 + -7x2 Combine like terms: 8x2 + -7x2 = 1x2 135 + -48x + 1x2 = -63 + 7x2 + 63 + -7x2 Reorder the terms: 135 + -48x + 1x2 = -63 + 63 + 7x2 + -7x2 Combine like terms: -63 + 63 = 0 135 + -48x + 1x2 = 0 + 7x2 + -7x2 135 + -48x + 1x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 135 + -48x + 1x2 = 0 Factor a trinomial. (3 + -1x)(45 + -1x) = 0Subproblem 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 '(45 + -1x)' equal to zero and attempt to solve: Simplifying 45 + -1x = 0 Solving 45 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + -1x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -1x = 0 + -45 -1x = 0 + -45 Combine like terms: 0 + -45 = -45 -1x = -45 Divide each side by '-1'. x = 45 Simplifying x = 45Solution
x = {3, 45}
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