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Simplifying 0 = 2x2 + -5x + 19 + -1(x + -5)(x + -5) Reorder the terms: 0 = 2x2 + -5x + 19 + -1(-5 + x)(x + -5) Reorder the terms: 0 = 2x2 + -5x + 19 + -1(-5 + x)(-5 + x) Multiply (-5 + x) * (-5 + x) 0 = 2x2 + -5x + 19 + -1(-5(-5 + x) + x(-5 + x)) 0 = 2x2 + -5x + 19 + -1((-5 * -5 + x * -5) + x(-5 + x)) 0 = 2x2 + -5x + 19 + -1((25 + -5x) + x(-5 + x)) 0 = 2x2 + -5x + 19 + -1(25 + -5x + (-5 * x + x * x)) 0 = 2x2 + -5x + 19 + -1(25 + -5x + (-5x + x2)) Combine like terms: -5x + -5x = -10x 0 = 2x2 + -5x + 19 + -1(25 + -10x + x2) 0 = 2x2 + -5x + 19 + (25 * -1 + -10x * -1 + x2 * -1) 0 = 2x2 + -5x + 19 + (-25 + 10x + -1x2) Reorder the terms: 0 = 19 + -25 + -5x + 10x + 2x2 + -1x2 Combine like terms: 19 + -25 = -6 0 = -6 + -5x + 10x + 2x2 + -1x2 Combine like terms: -5x + 10x = 5x 0 = -6 + 5x + 2x2 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 0 = -6 + 5x + 1x2 Solving 0 = -6 + 5x + 1x2 Solving for variable 'x'. Combine like terms: 0 + 6 = 6 6 + -5x + -1x2 = -6 + 5x + 1x2 + 6 + -5x + -1x2 Reorder the terms: 6 + -5x + -1x2 = -6 + 6 + 5x + -5x + 1x2 + -1x2 Combine like terms: -6 + 6 = 0 6 + -5x + -1x2 = 0 + 5x + -5x + 1x2 + -1x2 6 + -5x + -1x2 = 5x + -5x + 1x2 + -1x2 Combine like terms: 5x + -5x = 0 6 + -5x + -1x2 = 0 + 1x2 + -1x2 6 + -5x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 6 + -5x + -1x2 = 0 Factor a trinomial. (1 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {1, -6}
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