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Simplifying x2 + x2 + -10x + 25 = x2 + -20x + 100 Reorder the terms: 25 + -10x + x2 + x2 = x2 + -20x + 100 Combine like terms: x2 + x2 = 2x2 25 + -10x + 2x2 = x2 + -20x + 100 Reorder the terms: 25 + -10x + 2x2 = 100 + -20x + x2 Solving 25 + -10x + 2x2 = 100 + -20x + x2 Solving for variable 'x'. Reorder the terms: 25 + -100 + -10x + 20x + 2x2 + -1x2 = 100 + -20x + x2 + -100 + 20x + -1x2 Combine like terms: 25 + -100 = -75 -75 + -10x + 20x + 2x2 + -1x2 = 100 + -20x + x2 + -100 + 20x + -1x2 Combine like terms: -10x + 20x = 10x -75 + 10x + 2x2 + -1x2 = 100 + -20x + x2 + -100 + 20x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -75 + 10x + 1x2 = 100 + -20x + x2 + -100 + 20x + -1x2 Reorder the terms: -75 + 10x + 1x2 = 100 + -100 + -20x + 20x + x2 + -1x2 Combine like terms: 100 + -100 = 0 -75 + 10x + 1x2 = 0 + -20x + 20x + x2 + -1x2 -75 + 10x + 1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 -75 + 10x + 1x2 = 0 + x2 + -1x2 -75 + 10x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -75 + 10x + 1x2 = 0 Factor a trinomial. (-15 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 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 = {-15, 5}
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