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Simplifying x2 + (x + -1)(x + -1) = 41 Reorder the terms: x2 + (-1 + x)(x + -1) = 41 Reorder the terms: x2 + (-1 + x)(-1 + x) = 41 Multiply (-1 + x) * (-1 + x) x2 + (-1(-1 + x) + x(-1 + x)) = 41 x2 + ((-1 * -1 + x * -1) + x(-1 + x)) = 41 x2 + ((1 + -1x) + x(-1 + x)) = 41 x2 + (1 + -1x + (-1 * x + x * x)) = 41 x2 + (1 + -1x + (-1x + x2)) = 41 Combine like terms: -1x + -1x = -2x x2 + (1 + -2x + x2) = 41 Reorder the terms: 1 + -2x + x2 + x2 = 41 Combine like terms: x2 + x2 = 2x2 1 + -2x + 2x2 = 41 Solving 1 + -2x + 2x2 = 41 Solving for variable 'x'. Reorder the terms: 1 + -41 + -2x + 2x2 = 41 + -41 Combine like terms: 1 + -41 = -40 -40 + -2x + 2x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -40 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -1x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-4, 5}
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