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Simplifying (x + 5)(x + -5) = 8x + -41 Reorder the terms: (5 + x)(x + -5) = 8x + -41 Reorder the terms: (5 + x)(-5 + x) = 8x + -41 Multiply (5 + x) * (-5 + x) (5(-5 + x) + x(-5 + x)) = 8x + -41 ((-5 * 5 + x * 5) + x(-5 + x)) = 8x + -41 ((-25 + 5x) + x(-5 + x)) = 8x + -41 (-25 + 5x + (-5 * x + x * x)) = 8x + -41 (-25 + 5x + (-5x + x2)) = 8x + -41 Combine like terms: 5x + -5x = 0 (-25 + 0 + x2) = 8x + -41 (-25 + x2) = 8x + -41 Reorder the terms: -25 + x2 = -41 + 8x Solving -25 + x2 = -41 + 8x Solving for variable 'x'. Reorder the terms: -25 + 41 + -8x + x2 = -41 + 8x + 41 + -8x Combine like terms: -25 + 41 = 16 16 + -8x + x2 = -41 + 8x + 41 + -8x Reorder the terms: 16 + -8x + x2 = -41 + 41 + 8x + -8x Combine like terms: -41 + 41 = 0 16 + -8x + x2 = 0 + 8x + -8x 16 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 16 + -8x + x2 = 0 Factor a trinomial. (4 + -1x)(4 + -1x) = 0Subproblem 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 '(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 = 4Solution
x = {4, 4}
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