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Simplifying 7(x + -1)(2x + 1) = 0 Reorder the terms: 7(-1 + x)(2x + 1) = 0 Reorder the terms: 7(-1 + x)(1 + 2x) = 0 Multiply (-1 + x) * (1 + 2x) 7(-1(1 + 2x) + x(1 + 2x)) = 0 7((1 * -1 + 2x * -1) + x(1 + 2x)) = 0 7((-1 + -2x) + x(1 + 2x)) = 0 7(-1 + -2x + (1 * x + 2x * x)) = 0 7(-1 + -2x + (1x + 2x2)) = 0 Combine like terms: -2x + 1x = -1x 7(-1 + -1x + 2x2) = 0 (-1 * 7 + -1x * 7 + 2x2 * 7) = 0 (-7 + -7x + 14x2) = 0 Solving -7 + -7x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-1 + -1x + 2x2) = 0 Factor a trinomial. 7((-1 + -2x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 1
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 = -0.5Subproblem 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 = {-0.5, 1}
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