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Simplifying 10x2 + -84x + 162 = 0 Reorder the terms: 162 + -84x + 10x2 = 0 Solving 162 + -84x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -42x + 5x2) = 0 Factor a trinomial. 2((3 + -1x)(27 + -5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(27 + -5x)' equal to zero and attempt to solve: Simplifying 27 + -5x = 0 Solving 27 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -5x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -5x = 0 + -27 -5x = 0 + -27 Combine like terms: 0 + -27 = -27 -5x = -27 Divide each side by '-5'. x = 5.4 Simplifying x = 5.4Solution
x = {3, 5.4}
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