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Simplifying (7x + 6)(7x + 6) = 121 Reorder the terms: (6 + 7x)(7x + 6) = 121 Reorder the terms: (6 + 7x)(6 + 7x) = 121 Multiply (6 + 7x) * (6 + 7x) (6(6 + 7x) + 7x * (6 + 7x)) = 121 ((6 * 6 + 7x * 6) + 7x * (6 + 7x)) = 121 ((36 + 42x) + 7x * (6 + 7x)) = 121 (36 + 42x + (6 * 7x + 7x * 7x)) = 121 (36 + 42x + (42x + 49x2)) = 121 Combine like terms: 42x + 42x = 84x (36 + 84x + 49x2) = 121 Solving 36 + 84x + 49x2 = 121 Solving for variable 'x'. Reorder the terms: 36 + -121 + 84x + 49x2 = 121 + -121 Combine like terms: 36 + -121 = -85 -85 + 84x + 49x2 = 121 + -121 Combine like terms: 121 + -121 = 0 -85 + 84x + 49x2 = 0 Factor a trinomial. (-17 + -7x)(5 + -7x) = 0Subproblem 1
Set the factor '(-17 + -7x)' equal to zero and attempt to solve: Simplifying -17 + -7x = 0 Solving -17 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -7x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -7x = 0 + 17 -7x = 0 + 17 Combine like terms: 0 + 17 = 17 -7x = 17 Divide each side by '-7'. x = -2.428571429 Simplifying x = -2.428571429Subproblem 2
Set the factor '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 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 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Solution
x = {-2.428571429, 0.7142857143}
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