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Simplifying -23x2 + 107x + 5 = 65 Reorder the terms: 5 + 107x + -23x2 = 65 Solving 5 + 107x + -23x2 = 65 Solving for variable 'x'. Reorder the terms: 5 + -65 + 107x + -23x2 = 65 + -65 Combine like terms: 5 + -65 = -60 -60 + 107x + -23x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -60 + 107x + -23x2 = 0 Factor a trinomial. (-4 + x)(15 + -23x) = 0Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
Set the factor '(15 + -23x)' equal to zero and attempt to solve: Simplifying 15 + -23x = 0 Solving 15 + -23x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -23x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -23x = 0 + -15 -23x = 0 + -15 Combine like terms: 0 + -15 = -15 -23x = -15 Divide each side by '-23'. x = 0.652173913 Simplifying x = 0.652173913Solution
x = {4, 0.652173913}
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