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Simplifying (x + -5)(x + 5) = 24x Reorder the terms: (-5 + x)(x + 5) = 24x Reorder the terms: (-5 + x)(5 + x) = 24x Multiply (-5 + x) * (5 + x) (-5(5 + x) + x(5 + x)) = 24x ((5 * -5 + x * -5) + x(5 + x)) = 24x ((-25 + -5x) + x(5 + x)) = 24x (-25 + -5x + (5 * x + x * x)) = 24x (-25 + -5x + (5x + x2)) = 24x Combine like terms: -5x + 5x = 0 (-25 + 0 + x2) = 24x (-25 + x2) = 24x Solving -25 + x2 = 24x Solving for variable 'x'. Reorder the terms: -25 + -24x + x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -25 + -24x + x2 = 0 Factor a trinomial. (-1 + -1x)(25 + -1x) = 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 '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25Solution
x = {-1, 25}
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