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Simplifying 0 = 14x2 + -34x + 12 Reorder the terms: 0 = 12 + -34x + 14x2 Solving 0 = 12 + -34x + 14x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 34x + -14x2 = 12 + -34x + 14x2 + -12 + 34x + -14x2 Reorder the terms: -12 + 34x + -14x2 = 12 + -12 + -34x + 34x + 14x2 + -14x2 Combine like terms: 12 + -12 = 0 -12 + 34x + -14x2 = 0 + -34x + 34x + 14x2 + -14x2 -12 + 34x + -14x2 = -34x + 34x + 14x2 + -14x2 Combine like terms: -34x + 34x = 0 -12 + 34x + -14x2 = 0 + 14x2 + -14x2 -12 + 34x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -12 + 34x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 17x + -7x2) = 0 Factor a trinomial. 2((-2 + x)(3 + -7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve: Simplifying 3 + -7x = 0 Solving 3 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x = 0 + -3 -7x = 0 + -3 Combine like terms: 0 + -3 = -3 -7x = -3 Divide each side by '-7'. x = 0.4285714286 Simplifying x = 0.4285714286Solution
x = {2, 0.4285714286}
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