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Simplifying 80x + -4x2 = 400 Solving 80x + -4x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 80x + -4x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-100 + 20x + -1x2) = 0 Factor a trinomial. 4((-10 + x)(10 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {10, 10}
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