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Simplifying 10x2 + 4x = 32 Reorder the terms: 4x + 10x2 = 32 Solving 4x + 10x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 4x + 10x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 4x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 2x + 5x2) = 0 Factor a trinomial. 2((-2 + -1x)(8 + -5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 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 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {-2, 1.6}
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