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Simplifying (x + -5) + 10 = (x + 5)(x + -5) Reorder the terms: (-5 + x) + 10 = (x + 5)(x + -5) Remove parenthesis around (-5 + x) -5 + x + 10 = (x + 5)(x + -5) Reorder the terms: -5 + 10 + x = (x + 5)(x + -5) Combine like terms: -5 + 10 = 5 5 + x = (x + 5)(x + -5) Reorder the terms: 5 + x = (5 + x)(x + -5) Reorder the terms: 5 + x = (5 + x)(-5 + x) Multiply (5 + x) * (-5 + x) 5 + x = (5(-5 + x) + x(-5 + x)) 5 + x = ((-5 * 5 + x * 5) + x(-5 + x)) 5 + x = ((-25 + 5x) + x(-5 + x)) 5 + x = (-25 + 5x + (-5 * x + x * x)) 5 + x = (-25 + 5x + (-5x + x2)) Combine like terms: 5x + -5x = 0 5 + x = (-25 + 0 + x2) 5 + x = (-25 + x2) Solving 5 + x = -25 + x2 Solving for variable 'x'. Reorder the terms: 5 + 25 + x + -1x2 = -25 + x2 + 25 + -1x2 Combine like terms: 5 + 25 = 30 30 + x + -1x2 = -25 + x2 + 25 + -1x2 Reorder the terms: 30 + x + -1x2 = -25 + 25 + x2 + -1x2 Combine like terms: -25 + 25 = 0 30 + x + -1x2 = 0 + x2 + -1x2 30 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 30 + x + -1x2 = 0 Factor a trinomial. (6 + -1x)(5 + x) = 0Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 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 = {6, -5}
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