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Simplifying 12x = x2 + 35 Reorder the terms: 12x = 35 + x2 Solving 12x = 35 + x2 Solving for variable 'x'. Reorder the terms: -35 + 12x + -1x2 = 35 + x2 + -35 + -1x2 Reorder the terms: -35 + 12x + -1x2 = 35 + -35 + x2 + -1x2 Combine like terms: 35 + -35 = 0 -35 + 12x + -1x2 = 0 + x2 + -1x2 -35 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -35 + 12x + -1x2 = 0 Factor a trinomial. (-7 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Simplifying x = 7Subproblem 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 = {7, 5}
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