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Simplifying 4x2 + 12x = 4x + -2x2 + 14 Reorder the terms: 12x + 4x2 = 4x + -2x2 + 14 Reorder the terms: 12x + 4x2 = 14 + 4x + -2x2 Solving 12x + 4x2 = 14 + 4x + -2x2 Solving for variable 'x'. Reorder the terms: -14 + 12x + -4x + 4x2 + 2x2 = 14 + 4x + -2x2 + -14 + -4x + 2x2 Combine like terms: 12x + -4x = 8x -14 + 8x + 4x2 + 2x2 = 14 + 4x + -2x2 + -14 + -4x + 2x2 Combine like terms: 4x2 + 2x2 = 6x2 -14 + 8x + 6x2 = 14 + 4x + -2x2 + -14 + -4x + 2x2 Reorder the terms: -14 + 8x + 6x2 = 14 + -14 + 4x + -4x + -2x2 + 2x2 Combine like terms: 14 + -14 = 0 -14 + 8x + 6x2 = 0 + 4x + -4x + -2x2 + 2x2 -14 + 8x + 6x2 = 4x + -4x + -2x2 + 2x2 Combine like terms: 4x + -4x = 0 -14 + 8x + 6x2 = 0 + -2x2 + 2x2 -14 + 8x + 6x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -14 + 8x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 4x + 3x2) = 0 Factor a trinomial. 2((-7 + -3x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 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 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2.333333333, 1}
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