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Simplifying (2x + 13)(2x + 13) = 8 Reorder the terms: (13 + 2x)(2x + 13) = 8 Reorder the terms: (13 + 2x)(13 + 2x) = 8 Multiply (13 + 2x) * (13 + 2x) (13(13 + 2x) + 2x * (13 + 2x)) = 8 ((13 * 13 + 2x * 13) + 2x * (13 + 2x)) = 8 ((169 + 26x) + 2x * (13 + 2x)) = 8 (169 + 26x + (13 * 2x + 2x * 2x)) = 8 (169 + 26x + (26x + 4x2)) = 8 Combine like terms: 26x + 26x = 52x (169 + 52x + 4x2) = 8 Solving 169 + 52x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: 169 + -8 + 52x + 4x2 = 8 + -8 Combine like terms: 169 + -8 = 161 161 + 52x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 161 + 52x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 40.25 + 13x + x2 = 0 Move the constant term to the right: Add '-40.25' to each side of the equation. 40.25 + 13x + -40.25 + x2 = 0 + -40.25 Reorder the terms: 40.25 + -40.25 + 13x + x2 = 0 + -40.25 Combine like terms: 40.25 + -40.25 = 0.00 0.00 + 13x + x2 = 0 + -40.25 13x + x2 = 0 + -40.25 Combine like terms: 0 + -40.25 = -40.25 13x + x2 = -40.25 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -40.25 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -40.25 + 42.25 Combine like terms: -40.25 + 42.25 = 2 42.25 + 13x + x2 = 2 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 6.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 6.5 = 1.414213562 Simplifying x + 6.5 = 1.414213562 Reorder the terms: 6.5 + x = 1.414213562 Solving 6.5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 1.414213562 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 1.414213562 + -6.5 x = 1.414213562 + -6.5 Combine like terms: 1.414213562 + -6.5 = -5.085786438 x = -5.085786438 Simplifying x = -5.085786438Subproblem 2
x + 6.5 = -1.414213562 Simplifying x + 6.5 = -1.414213562 Reorder the terms: 6.5 + x = -1.414213562 Solving 6.5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -1.414213562 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -1.414213562 + -6.5 x = -1.414213562 + -6.5 Combine like terms: -1.414213562 + -6.5 = -7.914213562 x = -7.914213562 Simplifying x = -7.914213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.085786438, -7.914213562}
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