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Simplifying 4x2 + -70 = 5x2 + 19x Reorder the terms: -70 + 4x2 = 5x2 + 19x Reorder the terms: -70 + 4x2 = 19x + 5x2 Solving -70 + 4x2 = 19x + 5x2 Solving for variable 'x'. Reorder the terms: -70 + -19x + 4x2 + -5x2 = 19x + 5x2 + -19x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -70 + -19x + -1x2 = 19x + 5x2 + -19x + -5x2 Reorder the terms: -70 + -19x + -1x2 = 19x + -19x + 5x2 + -5x2 Combine like terms: 19x + -19x = 0 -70 + -19x + -1x2 = 0 + 5x2 + -5x2 -70 + -19x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -70 + -19x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(70 + 19x + x2) = 0 Factor a trinomial. -1((14 + x)(5 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-14, -5}
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