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Simplifying 0 = 10x2 + 28x + -174 Reorder the terms: 0 = -174 + 28x + 10x2 Solving 0 = -174 + 28x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 174 = 174 174 + -28x + -10x2 = -174 + 28x + 10x2 + 174 + -28x + -10x2 Reorder the terms: 174 + -28x + -10x2 = -174 + 174 + 28x + -28x + 10x2 + -10x2 Combine like terms: -174 + 174 = 0 174 + -28x + -10x2 = 0 + 28x + -28x + 10x2 + -10x2 174 + -28x + -10x2 = 28x + -28x + 10x2 + -10x2 Combine like terms: 28x + -28x = 0 174 + -28x + -10x2 = 0 + 10x2 + -10x2 174 + -28x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 174 + -28x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(87 + -14x + -5x2) = 0 Factor a trinomial. 2((3 + -1x)(29 + 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 '(29 + 5x)' equal to zero and attempt to solve: Simplifying 29 + 5x = 0 Solving 29 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 5x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 5x = 0 + -29 5x = 0 + -29 Combine like terms: 0 + -29 = -29 5x = -29 Divide each side by '5'. x = -5.8 Simplifying x = -5.8Solution
x = {3, -5.8}
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