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Simplifying 27 = x2 + -4x + 6 Reorder the terms: 27 = 6 + -4x + x2 Solving 27 = 6 + -4x + x2 Solving for variable 'x'. Combine like terms: 27 + -6 = 21 21 + 4x + -1x2 = 6 + -4x + x2 + -6 + 4x + -1x2 Reorder the terms: 21 + 4x + -1x2 = 6 + -6 + -4x + 4x + x2 + -1x2 Combine like terms: 6 + -6 = 0 21 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 21 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 21 + 4x + -1x2 = 0 + x2 + -1x2 21 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + 4x + -1x2 = 0 Factor a trinomial. (7 + -1x)(3 + x) = 0Subproblem 1
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 = 7Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {7, -3}
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