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Simplifying 8x2 + -5x = 7x2 + -8x + 54 Reorder the terms: -5x + 8x2 = 7x2 + -8x + 54 Reorder the terms: -5x + 8x2 = 54 + -8x + 7x2 Solving -5x + 8x2 = 54 + -8x + 7x2 Solving for variable 'x'. Reorder the terms: -54 + -5x + 8x + 8x2 + -7x2 = 54 + -8x + 7x2 + -54 + 8x + -7x2 Combine like terms: -5x + 8x = 3x -54 + 3x + 8x2 + -7x2 = 54 + -8x + 7x2 + -54 + 8x + -7x2 Combine like terms: 8x2 + -7x2 = 1x2 -54 + 3x + 1x2 = 54 + -8x + 7x2 + -54 + 8x + -7x2 Reorder the terms: -54 + 3x + 1x2 = 54 + -54 + -8x + 8x + 7x2 + -7x2 Combine like terms: 54 + -54 = 0 -54 + 3x + 1x2 = 0 + -8x + 8x + 7x2 + -7x2 -54 + 3x + 1x2 = -8x + 8x + 7x2 + -7x2 Combine like terms: -8x + 8x = 0 -54 + 3x + 1x2 = 0 + 7x2 + -7x2 -54 + 3x + 1x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -54 + 3x + 1x2 = 0 Factor a trinomial. (-9 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-9, 6}
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