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Simplifying 100x2 + -160x + 64 = 9 Reorder the terms: 64 + -160x + 100x2 = 9 Solving 64 + -160x + 100x2 = 9 Solving for variable 'x'. Reorder the terms: 64 + -9 + -160x + 100x2 = 9 + -9 Combine like terms: 64 + -9 = 55 55 + -160x + 100x2 = 9 + -9 Combine like terms: 9 + -9 = 0 55 + -160x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(11 + -32x + 20x2) = 0 Factor a trinomial. 5((1 + -2x)(11 + -10x)) = 0 Ignore the factor 5.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 '(11 + -10x)' equal to zero and attempt to solve: Simplifying 11 + -10x = 0 Solving 11 + -10x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -10x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -10x = 0 + -11 -10x = 0 + -11 Combine like terms: 0 + -11 = -11 -10x = -11 Divide each side by '-10'. x = 1.1 Simplifying x = 1.1Solution
x = {0.5, 1.1}
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