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Simplifying (2x + 6)(2x + 6) = 49 Reorder the terms: (6 + 2x)(2x + 6) = 49 Reorder the terms: (6 + 2x)(6 + 2x) = 49 Multiply (6 + 2x) * (6 + 2x) (6(6 + 2x) + 2x * (6 + 2x)) = 49 ((6 * 6 + 2x * 6) + 2x * (6 + 2x)) = 49 ((36 + 12x) + 2x * (6 + 2x)) = 49 (36 + 12x + (6 * 2x + 2x * 2x)) = 49 (36 + 12x + (12x + 4x2)) = 49 Combine like terms: 12x + 12x = 24x (36 + 24x + 4x2) = 49 Solving 36 + 24x + 4x2 = 49 Solving for variable 'x'. Reorder the terms: 36 + -49 + 24x + 4x2 = 49 + -49 Combine like terms: 36 + -49 = -13 -13 + 24x + 4x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -13 + 24x + 4x2 = 0 Factor a trinomial. (-13 + -2x)(1 + -2x) = 0Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve: Simplifying -13 + -2x = 0 Solving -13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x = 0 + 13 -2x = 0 + 13 Combine like terms: 0 + 13 = 13 -2x = 13 Divide each side by '-2'. x = -6.5 Simplifying x = -6.5Subproblem 2
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 = 0.5Solution
x = {-6.5, 0.5}
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