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Simplifying 4x + 2 + x2 + 2x + 1 = 9x2 + 4 + -12x + 3 Reorder the terms: 2 + 1 + 4x + 2x + x2 = 9x2 + 4 + -12x + 3 Combine like terms: 2 + 1 = 3 3 + 4x + 2x + x2 = 9x2 + 4 + -12x + 3 Combine like terms: 4x + 2x = 6x 3 + 6x + x2 = 9x2 + 4 + -12x + 3 Reorder the terms: 3 + 6x + x2 = 4 + 3 + -12x + 9x2 Combine like terms: 4 + 3 = 7 3 + 6x + x2 = 7 + -12x + 9x2 Solving 3 + 6x + x2 = 7 + -12x + 9x2 Solving for variable 'x'. Reorder the terms: 3 + -7 + 6x + 12x + x2 + -9x2 = 7 + -12x + 9x2 + -7 + 12x + -9x2 Combine like terms: 3 + -7 = -4 -4 + 6x + 12x + x2 + -9x2 = 7 + -12x + 9x2 + -7 + 12x + -9x2 Combine like terms: 6x + 12x = 18x -4 + 18x + x2 + -9x2 = 7 + -12x + 9x2 + -7 + 12x + -9x2 Combine like terms: x2 + -9x2 = -8x2 -4 + 18x + -8x2 = 7 + -12x + 9x2 + -7 + 12x + -9x2 Reorder the terms: -4 + 18x + -8x2 = 7 + -7 + -12x + 12x + 9x2 + -9x2 Combine like terms: 7 + -7 = 0 -4 + 18x + -8x2 = 0 + -12x + 12x + 9x2 + -9x2 -4 + 18x + -8x2 = -12x + 12x + 9x2 + -9x2 Combine like terms: -12x + 12x = 0 -4 + 18x + -8x2 = 0 + 9x2 + -9x2 -4 + 18x + -8x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -4 + 18x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 9x + -4x2) = 0 Factor a trinomial. 2((-2 + x)(1 + -4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {2, 0.25}
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