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Simplifying 9x2 + 40 = 45x + 4x2 Reorder the terms: 40 + 9x2 = 45x + 4x2 Solving 40 + 9x2 = 45x + 4x2 Solving for variable 'x'. Reorder the terms: 40 + -45x + 9x2 + -4x2 = 45x + 4x2 + -45x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 40 + -45x + 5x2 = 45x + 4x2 + -45x + -4x2 Reorder the terms: 40 + -45x + 5x2 = 45x + -45x + 4x2 + -4x2 Combine like terms: 45x + -45x = 0 40 + -45x + 5x2 = 0 + 4x2 + -4x2 40 + -45x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 40 + -45x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(8 + -9x + x2) = 0 Factor a trinomial. 5((1 + -1x)(8 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {1, 8}
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