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Simplifying 7x = x2 + 10 Reorder the terms: 7x = 10 + x2 Solving 7x = 10 + x2 Solving for variable 'x'. Reorder the terms: -10 + 7x + -1x2 = 10 + x2 + -10 + -1x2 Reorder the terms: -10 + 7x + -1x2 = 10 + -10 + x2 + -1x2 Combine like terms: 10 + -10 = 0 -10 + 7x + -1x2 = 0 + x2 + -1x2 -10 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + 7x + -1x2 = 0 Factor a trinomial. (-5 + x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {5, 2}
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