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Simplifying 10x2 + 22x = 32 Reorder the terms: 22x + 10x2 = 32 Solving 22x + 10x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 22x + 10x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 22x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 11x + 5x2) = 0 Factor a trinomial. 2((-16 + -5x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -5x)' equal to zero and attempt to solve: Simplifying -16 + -5x = 0 Solving -16 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -5x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5x = 0 + 16 -5x = 0 + 16 Combine like terms: 0 + 16 = 16 -5x = 16 Divide each side by '-5'. x = -3.2 Simplifying x = -3.2Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-3.2, 1}
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