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Simplifying 4x2 + -19 = 5x2 + 20x Reorder the terms: -19 + 4x2 = 5x2 + 20x Reorder the terms: -19 + 4x2 = 20x + 5x2 Solving -19 + 4x2 = 20x + 5x2 Solving for variable 'x'. Reorder the terms: -19 + -20x + 4x2 + -5x2 = 20x + 5x2 + -20x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -19 + -20x + -1x2 = 20x + 5x2 + -20x + -5x2 Reorder the terms: -19 + -20x + -1x2 = 20x + -20x + 5x2 + -5x2 Combine like terms: 20x + -20x = 0 -19 + -20x + -1x2 = 0 + 5x2 + -5x2 -19 + -20x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -19 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(19 + 20x + x2) = 0 Factor a trinomial. -1((19 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Simplifying x = -19Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-19, -1}
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