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Simplifying 76x2 = -96 + -172x + 6x2 Solving 76x2 = -96 + -172x + 6x2 Solving for variable 'x'. Reorder the terms: 96 + 172x + 76x2 + -6x2 = -96 + -172x + 6x2 + 96 + 172x + -6x2 Combine like terms: 76x2 + -6x2 = 70x2 96 + 172x + 70x2 = -96 + -172x + 6x2 + 96 + 172x + -6x2 Reorder the terms: 96 + 172x + 70x2 = -96 + 96 + -172x + 172x + 6x2 + -6x2 Combine like terms: -96 + 96 = 0 96 + 172x + 70x2 = 0 + -172x + 172x + 6x2 + -6x2 96 + 172x + 70x2 = -172x + 172x + 6x2 + -6x2 Combine like terms: -172x + 172x = 0 96 + 172x + 70x2 = 0 + 6x2 + -6x2 96 + 172x + 70x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 96 + 172x + 70x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + 86x + 35x2) = 0 Factor a trinomial. 2((8 + 5x)(6 + 7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 5x)' equal to zero and attempt to solve: Simplifying 8 + 5x = 0 Solving 8 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5x = 0 + -8 5x = 0 + -8 Combine like terms: 0 + -8 = -8 5x = -8 Divide each side by '5'. x = -1.6 Simplifying x = -1.6Subproblem 2
Set the factor '(6 + 7x)' equal to zero and attempt to solve: Simplifying 6 + 7x = 0 Solving 6 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7x = 0 + -6 7x = 0 + -6 Combine like terms: 0 + -6 = -6 7x = -6 Divide each side by '7'. x = -0.8571428571 Simplifying x = -0.8571428571Solution
x = {-1.6, -0.8571428571}
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