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Simplifying 900 = 4x(40 + x) 900 = (40 * 4x + x * 4x) 900 = (160x + 4x2) Solving 900 = 160x + 4x2 Solving for variable 'x'. Reorder the terms: 900 + -160x + -4x2 = 160x + -160x + 4x2 + -4x2 Combine like terms: 160x + -160x = 0 900 + -160x + -4x2 = 0 + 4x2 + -4x2 900 + -160x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 900 + -160x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(225 + -40x + -1x2) = 0 Factor a trinomial. 4((5 + -1x)(45 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(45 + x)' equal to zero and attempt to solve: Simplifying 45 + x = 0 Solving 45 + x = 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 + x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + x = 0 + -45 x = 0 + -45 Combine like terms: 0 + -45 = -45 x = -45 Simplifying x = -45Solution
x = {5, -45}
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