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Simplifying -100 + 17x = 4x2 + -23x Reorder the terms: -100 + 17x = -23x + 4x2 Solving -100 + 17x = -23x + 4x2 Solving for variable 'x'. Combine like terms: 17x + 23x = 40x -100 + 40x + -4x2 = -23x + 4x2 + 23x + -4x2 Reorder the terms: -100 + 40x + -4x2 = -23x + 23x + 4x2 + -4x2 Combine like terms: -23x + 23x = 0 -100 + 40x + -4x2 = 0 + 4x2 + -4x2 -100 + 40x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -100 + 40x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 10x + -1x2) = 0 Factor a trinomial. 4((-5 + x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
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 = 5Solution
x = {5, 5}
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