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Simplifying 2x2 + 28 = x2 + 11x Reorder the terms: 28 + 2x2 = x2 + 11x Reorder the terms: 28 + 2x2 = 11x + x2 Solving 28 + 2x2 = 11x + x2 Solving for variable 'x'. Reorder the terms: 28 + -11x + 2x2 + -1x2 = 11x + x2 + -11x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 28 + -11x + 1x2 = 11x + x2 + -11x + -1x2 Reorder the terms: 28 + -11x + 1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 28 + -11x + 1x2 = 0 + x2 + -1x2 28 + -11x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 28 + -11x + 1x2 = 0 Factor a trinomial. (4 + -1x)(7 + -1x) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {4, 7}
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