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Simplifying 5 = x2 + -10x + 30 Reorder the terms: 5 = 30 + -10x + x2 Solving 5 = 30 + -10x + x2 Solving for variable 'x'. Combine like terms: 5 + -30 = -25 -25 + 10x + -1x2 = 30 + -10x + x2 + -30 + 10x + -1x2 Reorder the terms: -25 + 10x + -1x2 = 30 + -30 + -10x + 10x + x2 + -1x2 Combine like terms: 30 + -30 = 0 -25 + 10x + -1x2 = 0 + -10x + 10x + x2 + -1x2 -25 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 -25 + 10x + -1x2 = 0 + x2 + -1x2 -25 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -25 + 10x + -1x2 = 0 Factor a trinomial. (-5 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 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 = {5, 5}
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