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Simplifying 4x + 110 = x2 + 5x Reorder the terms: 110 + 4x = x2 + 5x Reorder the terms: 110 + 4x = 5x + x2 Solving 110 + 4x = 5x + x2 Solving for variable 'x'. Combine like terms: 4x + -5x = -1x 110 + -1x + -1x2 = 5x + x2 + -5x + -1x2 Reorder the terms: 110 + -1x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 110 + -1x + -1x2 = 0 + x2 + -1x2 110 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 110 + -1x + -1x2 = 0 Factor a trinomial. (10 + -1x)(11 + x) = 0Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Simplifying x = -11Solution
x = {10, -11}
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