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Simplifying (-10x + 4)(7x + -14) + (9x + 12)(-10x + 4) = 0 Reorder the terms: (4 + -10x)(7x + -14) + (9x + 12)(-10x + 4) = 0 Reorder the terms: (4 + -10x)(-14 + 7x) + (9x + 12)(-10x + 4) = 0 Multiply (4 + -10x) * (-14 + 7x) (4(-14 + 7x) + -10x * (-14 + 7x)) + (9x + 12)(-10x + 4) = 0 ((-14 * 4 + 7x * 4) + -10x * (-14 + 7x)) + (9x + 12)(-10x + 4) = 0 ((-56 + 28x) + -10x * (-14 + 7x)) + (9x + 12)(-10x + 4) = 0 (-56 + 28x + (-14 * -10x + 7x * -10x)) + (9x + 12)(-10x + 4) = 0 (-56 + 28x + (140x + -70x2)) + (9x + 12)(-10x + 4) = 0 Combine like terms: 28x + 140x = 168x (-56 + 168x + -70x2) + (9x + 12)(-10x + 4) = 0 Reorder the terms: -56 + 168x + -70x2 + (12 + 9x)(-10x + 4) = 0 Reorder the terms: -56 + 168x + -70x2 + (12 + 9x)(4 + -10x) = 0 Multiply (12 + 9x) * (4 + -10x) -56 + 168x + -70x2 + (12(4 + -10x) + 9x * (4 + -10x)) = 0 -56 + 168x + -70x2 + ((4 * 12 + -10x * 12) + 9x * (4 + -10x)) = 0 -56 + 168x + -70x2 + ((48 + -120x) + 9x * (4 + -10x)) = 0 -56 + 168x + -70x2 + (48 + -120x + (4 * 9x + -10x * 9x)) = 0 -56 + 168x + -70x2 + (48 + -120x + (36x + -90x2)) = 0 Combine like terms: -120x + 36x = -84x -56 + 168x + -70x2 + (48 + -84x + -90x2) = 0 Reorder the terms: -56 + 48 + 168x + -84x + -70x2 + -90x2 = 0 Combine like terms: -56 + 48 = -8 -8 + 168x + -84x + -70x2 + -90x2 = 0 Combine like terms: 168x + -84x = 84x -8 + 84x + -70x2 + -90x2 = 0 Combine like terms: -70x2 + -90x2 = -160x2 -8 + 84x + -160x2 = 0 Solving -8 + 84x + -160x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 21x + -40x2) = 0 Factor a trinomial. 4((-2 + 5x)(1 + -8x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 5x)' equal to zero and attempt to solve: Simplifying -2 + 5x = 0 Solving -2 + 5x = 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 + 5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x = 0 + 2 5x = 0 + 2 Combine like terms: 0 + 2 = 2 5x = 2 Divide each side by '5'. x = 0.4 Simplifying x = 0.4Subproblem 2
Set the factor '(1 + -8x)' equal to zero and attempt to solve: Simplifying 1 + -8x = 0 Solving 1 + -8x = 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 + -8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x = 0 + -1 -8x = 0 + -1 Combine like terms: 0 + -1 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125Solution
x = {0.4, 0.125}
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