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Simplifying -4x2 + -7x + 61 = -1x + 7 Reorder the terms: 61 + -7x + -4x2 = -1x + 7 Reorder the terms: 61 + -7x + -4x2 = 7 + -1x Solving 61 + -7x + -4x2 = 7 + -1x Solving for variable 'x'. Reorder the terms: 61 + -7 + -7x + x + -4x2 = 7 + -1x + -7 + x Combine like terms: 61 + -7 = 54 54 + -7x + x + -4x2 = 7 + -1x + -7 + x Combine like terms: -7x + x = -6x 54 + -6x + -4x2 = 7 + -1x + -7 + x Reorder the terms: 54 + -6x + -4x2 = 7 + -7 + -1x + x Combine like terms: 7 + -7 = 0 54 + -6x + -4x2 = 0 + -1x + x 54 + -6x + -4x2 = -1x + x Combine like terms: -1x + x = 0 54 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -3x + -2x2) = 0 Factor a trinomial. 2((3 + -1x)(9 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Solution
x = {3, -4.5}
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