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Simplifying 4x(7 + 2x) + -1(2 + 4x) = 12 (7 * 4x + 2x * 4x) + -1(2 + 4x) = 12 (28x + 8x2) + -1(2 + 4x) = 12 28x + 8x2 + (2 * -1 + 4x * -1) = 12 28x + 8x2 + (-2 + -4x) = 12 Reorder the terms: -2 + 28x + -4x + 8x2 = 12 Combine like terms: 28x + -4x = 24x -2 + 24x + 8x2 = 12 Solving -2 + 24x + 8x2 = 12 Solving for variable 'x'. Reorder the terms: -2 + -12 + 24x + 8x2 = 12 + -12 Combine like terms: -2 + -12 = -14 -14 + 24x + 8x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -14 + 24x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 12x + 4x2) = 0 Factor a trinomial. 2((-7 + -2x)(1 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-3.5, 0.5}
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