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Simplifying 10x2 + 20x + -78 = 2 Reorder the terms: -78 + 20x + 10x2 = 2 Solving -78 + 20x + 10x2 = 2 Solving for variable 'x'. Reorder the terms: -78 + -2 + 20x + 10x2 = 2 + -2 Combine like terms: -78 + -2 = -80 -80 + 20x + 10x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -80 + 20x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-8 + 2x + x2) = 0 Factor a trinomial. 10((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 10.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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