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Simplifying 5x2 + 10x + 7 = 47 Reorder the terms: 7 + 10x + 5x2 = 47 Solving 7 + 10x + 5x2 = 47 Solving for variable 'x'. Reorder the terms: 7 + -47 + 10x + 5x2 = 47 + -47 Combine like terms: 7 + -47 = -40 -40 + 10x + 5x2 = 47 + -47 Combine like terms: 47 + -47 = 0 -40 + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + 2x + x2) = 0 Factor a trinomial. 5((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 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 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
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 = 2Solution
x = {-4, 2}
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