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Simplifying 3x + -5 = x2 + -10x + 25 Reorder the terms: -5 + 3x = x2 + -10x + 25 Reorder the terms: -5 + 3x = 25 + -10x + x2 Solving -5 + 3x = 25 + -10x + x2 Solving for variable 'x'. Reorder the terms: -5 + -25 + 3x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Combine like terms: -5 + -25 = -30 -30 + 3x + 10x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Combine like terms: 3x + 10x = 13x -30 + 13x + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Reorder the terms: -30 + 13x + -1x2 = 25 + -25 + -10x + 10x + x2 + -1x2 Combine like terms: 25 + -25 = 0 -30 + 13x + -1x2 = 0 + -10x + 10x + x2 + -1x2 -30 + 13x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 -30 + 13x + -1x2 = 0 + x2 + -1x2 -30 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -30 + 13x + -1x2 = 0 Factor a trinomial. (-10 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {10, 3}
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