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Simplifying 40x2 + -12 = -2x2 + 78x Reorder the terms: -12 + 40x2 = -2x2 + 78x Reorder the terms: -12 + 40x2 = 78x + -2x2 Solving -12 + 40x2 = 78x + -2x2 Solving for variable 'x'. Reorder the terms: -12 + -78x + 40x2 + 2x2 = 78x + -2x2 + -78x + 2x2 Combine like terms: 40x2 + 2x2 = 42x2 -12 + -78x + 42x2 = 78x + -2x2 + -78x + 2x2 Reorder the terms: -12 + -78x + 42x2 = 78x + -78x + -2x2 + 2x2 Combine like terms: 78x + -78x = 0 -12 + -78x + 42x2 = 0 + -2x2 + 2x2 -12 + -78x + 42x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -12 + -78x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + -13x + 7x2) = 0 Factor a trinomial. 6((-1 + -7x)(2 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -7x)' equal to zero and attempt to solve: Simplifying -1 + -7x = 0 Solving -1 + -7x = 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 + -7x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7x = 0 + 1 -7x = 0 + 1 Combine like terms: 0 + 1 = 1 -7x = 1 Divide each side by '-7'. x = -0.1428571429 Simplifying x = -0.1428571429Subproblem 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 = {-0.1428571429, 2}
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