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Simplifying x2 + -26x + 161 = 0 Reorder the terms: 161 + -26x + x2 = 0 Solving 161 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-161' to each side of the equation. 161 + -26x + -161 + x2 = 0 + -161 Reorder the terms: 161 + -161 + -26x + x2 = 0 + -161 Combine like terms: 161 + -161 = 0 0 + -26x + x2 = 0 + -161 -26x + x2 = 0 + -161 Combine like terms: 0 + -161 = -161 -26x + x2 = -161 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 = -161 + 169 Reorder the terms: 169 + -26x + x2 = -161 + 169 Combine like terms: -161 + 169 = 8 169 + -26x + x2 = 8 Factor a perfect square on the left side: (x + -13)(x + -13) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -13) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -13 = 2.828427125 Simplifying x + -13 = 2.828427125 Reorder the terms: -13 + x = 2.828427125 Solving -13 + x = 2.828427125 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 = 2.828427125 + 13 Combine like terms: -13 + 13 = 0 0 + x = 2.828427125 + 13 x = 2.828427125 + 13 Combine like terms: 2.828427125 + 13 = 15.828427125 x = 15.828427125 Simplifying x = 15.828427125Subproblem 2
x + -13 = -2.828427125 Simplifying x + -13 = -2.828427125 Reorder the terms: -13 + x = -2.828427125 Solving -13 + x = -2.828427125 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 = -2.828427125 + 13 Combine like terms: -13 + 13 = 0 0 + x = -2.828427125 + 13 x = -2.828427125 + 13 Combine like terms: -2.828427125 + 13 = 10.171572875 x = 10.171572875 Simplifying x = 10.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.828427125, 10.171572875}
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