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Simplifying 10 = x2 + -7x + 30 + -2x Reorder the terms: 10 = 30 + -7x + -2x + x2 Combine like terms: -7x + -2x = -9x 10 = 30 + -9x + x2 Solving 10 = 30 + -9x + x2 Solving for variable 'x'. Combine like terms: 10 + -30 = -20 -20 + 9x + -1x2 = 30 + -9x + x2 + -30 + 9x + -1x2 Reorder the terms: -20 + 9x + -1x2 = 30 + -30 + -9x + 9x + x2 + -1x2 Combine like terms: 30 + -30 = 0 -20 + 9x + -1x2 = 0 + -9x + 9x + x2 + -1x2 -20 + 9x + -1x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 -20 + 9x + -1x2 = 0 + x2 + -1x2 -20 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + 9x + -1x2 = 0 Factor a trinomial. (-5 + x)(4 + -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 '(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 = {5, 4}
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