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Simplifying 11 = x2 + -4x + -21 Reorder the terms: 11 = -21 + -4x + x2 Solving 11 = -21 + -4x + x2 Solving for variable 'x'. Combine like terms: 11 + 21 = 32 32 + 4x + -1x2 = -21 + -4x + x2 + 21 + 4x + -1x2 Reorder the terms: 32 + 4x + -1x2 = -21 + 21 + -4x + 4x + x2 + -1x2 Combine like terms: -21 + 21 = 0 32 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 32 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 32 + 4x + -1x2 = 0 + x2 + -1x2 32 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 32 + 4x + -1x2 = 0 Factor a trinomial. (8 + -1x)(4 + x) = 0Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {8, -4}
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