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Simplifying 4(4x + -7)(2x + 7) = 0 Reorder the terms: 4(-7 + 4x)(2x + 7) = 0 Reorder the terms: 4(-7 + 4x)(7 + 2x) = 0 Multiply (-7 + 4x) * (7 + 2x) 4(-7(7 + 2x) + 4x * (7 + 2x)) = 0 4((7 * -7 + 2x * -7) + 4x * (7 + 2x)) = 0 4((-49 + -14x) + 4x * (7 + 2x)) = 0 4(-49 + -14x + (7 * 4x + 2x * 4x)) = 0 4(-49 + -14x + (28x + 8x2)) = 0 Combine like terms: -14x + 28x = 14x 4(-49 + 14x + 8x2) = 0 (-49 * 4 + 14x * 4 + 8x2 * 4) = 0 (-196 + 56x + 32x2) = 0 Solving -196 + 56x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-49 + 14x + 8x2) = 0 Factor a trinomial. 4((-7 + -2x)(7 + -4x)) = 0 Ignore the factor 4.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 '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 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 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Solution
x = {-3.5, 1.75}
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