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Simplifying 5x(2x + -9) = x2 + -54 Reorder the terms: 5x(-9 + 2x) = x2 + -54 (-9 * 5x + 2x * 5x) = x2 + -54 (-45x + 10x2) = x2 + -54 Reorder the terms: -45x + 10x2 = -54 + x2 Solving -45x + 10x2 = -54 + x2 Solving for variable 'x'. Reorder the terms: 54 + -45x + 10x2 + -1x2 = -54 + x2 + 54 + -1x2 Combine like terms: 10x2 + -1x2 = 9x2 54 + -45x + 9x2 = -54 + x2 + 54 + -1x2 Reorder the terms: 54 + -45x + 9x2 = -54 + 54 + x2 + -1x2 Combine like terms: -54 + 54 = 0 54 + -45x + 9x2 = 0 + x2 + -1x2 54 + -45x + 9x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + -45x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(6 + -5x + x2) = 0 Factor a trinomial. 9((2 + -1x)(3 + -1x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
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 = 3Solution
x = {2, 3}
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