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Simplifying x2 + 26x + -23 = 0 Reorder the terms: -23 + 26x + x2 = 0 Solving -23 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 26x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 26x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 26x + x2 = 0 + 23 26x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 26x + x2 = 23 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 = 23 + 169 Reorder the terms: 169 + 26x + x2 = 23 + 169 Combine like terms: 23 + 169 = 192 169 + 26x + x2 = 192 Factor a perfect square on the left side: (x + 13)(x + 13) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x + 13) equal to 13.856406461 and -13.856406461.Subproblem 1
x + 13 = 13.856406461 Simplifying x + 13 = 13.856406461 Reorder the terms: 13 + x = 13.856406461 Solving 13 + x = 13.856406461 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 = 13.856406461 + -13 Combine like terms: 13 + -13 = 0 0 + x = 13.856406461 + -13 x = 13.856406461 + -13 Combine like terms: 13.856406461 + -13 = 0.856406461 x = 0.856406461 Simplifying x = 0.856406461Subproblem 2
x + 13 = -13.856406461 Simplifying x + 13 = -13.856406461 Reorder the terms: 13 + x = -13.856406461 Solving 13 + x = -13.856406461 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 = -13.856406461 + -13 Combine like terms: 13 + -13 = 0 0 + x = -13.856406461 + -13 x = -13.856406461 + -13 Combine like terms: -13.856406461 + -13 = -26.856406461 x = -26.856406461 Simplifying x = -26.856406461Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.856406461, -26.856406461}
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