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Simplifying (x + -13)(x + -13) = 20 Reorder the terms: (-13 + x)(x + -13) = 20 Reorder the terms: (-13 + x)(-13 + x) = 20 Multiply (-13 + x) * (-13 + x) (-13(-13 + x) + x(-13 + x)) = 20 ((-13 * -13 + x * -13) + x(-13 + x)) = 20 ((169 + -13x) + x(-13 + x)) = 20 (169 + -13x + (-13 * x + x * x)) = 20 (169 + -13x + (-13x + x2)) = 20 Combine like terms: -13x + -13x = -26x (169 + -26x + x2) = 20 Solving 169 + -26x + x2 = 20 Solving for variable 'x'. Reorder the terms: 169 + -20 + -26x + x2 = 20 + -20 Combine like terms: 169 + -20 = 149 149 + -26x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 149 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-149' to each side of the equation. 149 + -26x + -149 + x2 = 0 + -149 Reorder the terms: 149 + -149 + -26x + x2 = 0 + -149 Combine like terms: 149 + -149 = 0 0 + -26x + x2 = 0 + -149 -26x + x2 = 0 + -149 Combine like terms: 0 + -149 = -149 -26x + x2 = -149 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 = -149 + 169 Reorder the terms: 169 + -26x + x2 = -149 + 169 Combine like terms: -149 + 169 = 20 169 + -26x + x2 = 20 Factor a perfect square on the left side: (x + -13)(x + -13) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -13) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -13 = 4.472135955 Simplifying x + -13 = 4.472135955 Reorder the terms: -13 + x = 4.472135955 Solving -13 + x = 4.472135955 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 = 4.472135955 + 13 Combine like terms: -13 + 13 = 0 0 + x = 4.472135955 + 13 x = 4.472135955 + 13 Combine like terms: 4.472135955 + 13 = 17.472135955 x = 17.472135955 Simplifying x = 17.472135955Subproblem 2
x + -13 = -4.472135955 Simplifying x + -13 = -4.472135955 Reorder the terms: -13 + x = -4.472135955 Solving -13 + x = -4.472135955 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 = -4.472135955 + 13 Combine like terms: -13 + 13 = 0 0 + x = -4.472135955 + 13 x = -4.472135955 + 13 Combine like terms: -4.472135955 + 13 = 8.527864045 x = 8.527864045 Simplifying x = 8.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.472135955, 8.527864045}
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