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Simplifying 7x2 + -84x + 251 = 6 Reorder the terms: 251 + -84x + 7x2 = 6 Solving 251 + -84x + 7x2 = 6 Solving for variable 'x'. Reorder the terms: 251 + -6 + -84x + 7x2 = 6 + -6 Combine like terms: 251 + -6 = 245 245 + -84x + 7x2 = 6 + -6 Combine like terms: 6 + -6 = 0 245 + -84x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(35 + -12x + x2) = 0 Factor a trinomial. 7((5 + -1x)(7 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {5, 7}
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