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Simplifying (13x + 1)(13x + 1) = (1)(1) + (11x)(11x) Reorder the terms: (1 + 13x)(13x + 1) = (1)(1) + (11x)(11x) Reorder the terms: (1 + 13x)(1 + 13x) = (1)(1) + (11x)(11x) Multiply (1 + 13x) * (1 + 13x) (1(1 + 13x) + 13x * (1 + 13x)) = (1)(1) + (11x)(11x) ((1 * 1 + 13x * 1) + 13x * (1 + 13x)) = (1)(1) + (11x)(11x) ((1 + 13x) + 13x * (1 + 13x)) = (1)(1) + (11x)(11x) (1 + 13x + (1 * 13x + 13x * 13x)) = (1)(1) + (11x)(11x) (1 + 13x + (13x + 169x2)) = (1)(1) + (11x)(11x) Combine like terms: 13x + 13x = 26x (1 + 26x + 169x2) = (1)(1) + (11x)(11x) Multiply 1 * 1 1 + 26x + 169x2 = 1 + (11x)(11x) Remove parenthesis around (11x) 1 + 26x + 169x2 = 1 + 11x(11x) Remove parenthesis around (11x) 1 + 26x + 169x2 = 1 + 11x * 11x Reorder the terms for easier multiplication: 1 + 26x + 169x2 = 1 + 11 * 11x * x Multiply 11 * 11 1 + 26x + 169x2 = 1 + 121x * x Multiply x * x 1 + 26x + 169x2 = 1 + 121x2 Add '-1' to each side of the equation. 1 + 26x + -1 + 169x2 = 1 + -1 + 121x2 Reorder the terms: 1 + -1 + 26x + 169x2 = 1 + -1 + 121x2 Combine like terms: 1 + -1 = 0 0 + 26x + 169x2 = 1 + -1 + 121x2 26x + 169x2 = 1 + -1 + 121x2 Combine like terms: 1 + -1 = 0 26x + 169x2 = 0 + 121x2 26x + 169x2 = 121x2 Solving 26x + 169x2 = 121x2 Solving for variable 'x'. Combine like terms: 169x2 + -121x2 = 48x2 26x + 48x2 = 121x2 + -121x2 Combine like terms: 121x2 + -121x2 = 0 26x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(13 + 24x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(13 + 24x)' equal to zero and attempt to solve: Simplifying 13 + 24x = 0 Solving 13 + 24x = 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 + 24x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 24x = 0 + -13 24x = 0 + -13 Combine like terms: 0 + -13 = -13 24x = -13 Divide each side by '24'. x = -0.5416666667 Simplifying x = -0.5416666667Solution
x = {0, -0.5416666667}
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