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Simplifying x2 + 26x = -104 Reorder the terms: 26x + x2 = -104 Solving 26x + x2 = -104 Solving for variable 'x'. Reorder the terms: 104 + 26x + x2 = -104 + 104 Combine like terms: -104 + 104 = 0 104 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + 26x + -104 + x2 = 0 + -104 Reorder the terms: 104 + -104 + 26x + x2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + 26x + x2 = 0 + -104 26x + x2 = 0 + -104 Combine like terms: 0 + -104 = -104 26x + x2 = -104 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 = -104 + 169 Reorder the terms: 169 + 26x + x2 = -104 + 169 Combine like terms: -104 + 169 = 65 169 + 26x + x2 = 65 Factor a perfect square on the left side: (x + 13)(x + 13) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + 13) equal to 8.062257748 and -8.062257748.Subproblem 1
x + 13 = 8.062257748 Simplifying x + 13 = 8.062257748 Reorder the terms: 13 + x = 8.062257748 Solving 13 + x = 8.062257748 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 = 8.062257748 + -13 Combine like terms: 13 + -13 = 0 0 + x = 8.062257748 + -13 x = 8.062257748 + -13 Combine like terms: 8.062257748 + -13 = -4.937742252 x = -4.937742252 Simplifying x = -4.937742252Subproblem 2
x + 13 = -8.062257748 Simplifying x + 13 = -8.062257748 Reorder the terms: 13 + x = -8.062257748 Solving 13 + x = -8.062257748 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 = -8.062257748 + -13 Combine like terms: 13 + -13 = 0 0 + x = -8.062257748 + -13 x = -8.062257748 + -13 Combine like terms: -8.062257748 + -13 = -21.062257748 x = -21.062257748 Simplifying x = -21.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.937742252, -21.062257748}
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