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Simplifying (x + 13)(x + 13) = 7 Reorder the terms: (13 + x)(x + 13) = 7 Reorder the terms: (13 + x)(13 + x) = 7 Multiply (13 + x) * (13 + x) (13(13 + x) + x(13 + x)) = 7 ((13 * 13 + x * 13) + x(13 + x)) = 7 ((169 + 13x) + x(13 + x)) = 7 (169 + 13x + (13 * x + x * x)) = 7 (169 + 13x + (13x + x2)) = 7 Combine like terms: 13x + 13x = 26x (169 + 26x + x2) = 7 Solving 169 + 26x + x2 = 7 Solving for variable 'x'. Reorder the terms: 169 + -7 + 26x + x2 = 7 + -7 Combine like terms: 169 + -7 = 162 162 + 26x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 162 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-162' to each side of the equation. 162 + 26x + -162 + x2 = 0 + -162 Reorder the terms: 162 + -162 + 26x + x2 = 0 + -162 Combine like terms: 162 + -162 = 0 0 + 26x + x2 = 0 + -162 26x + x2 = 0 + -162 Combine like terms: 0 + -162 = -162 26x + x2 = -162 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -162 + 169 Reorder the terms: 169 + 26x + x2 = -162 + 169 Combine like terms: -162 + 169 = 7 169 + 26x + x2 = 7 Factor a perfect square on the left side: (x + 13)(x + 13) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 13) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 13 = 2.645751311 Simplifying x + 13 = 2.645751311 Reorder the terms: 13 + x = 2.645751311 Solving 13 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 2.645751311 + -13 Combine like terms: 13 + -13 = 0 0 + x = 2.645751311 + -13 x = 2.645751311 + -13 Combine like terms: 2.645751311 + -13 = -10.354248689 x = -10.354248689 Simplifying x = -10.354248689Subproblem 2
x + 13 = -2.645751311 Simplifying x + 13 = -2.645751311 Reorder the terms: 13 + x = -2.645751311 Solving 13 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -2.645751311 + -13 Combine like terms: 13 + -13 = 0 0 + x = -2.645751311 + -13 x = -2.645751311 + -13 Combine like terms: -2.645751311 + -13 = -15.645751311 x = -15.645751311 Simplifying x = -15.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.354248689, -15.645751311}
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