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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 = 146 169 + 26x + x2 = 146 Factor a perfect square on the left side: (x + 13)(x + 13) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 13) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 13 = 12.083045974 Simplifying x + 13 = 12.083045974 Reorder the terms: 13 + x = 12.083045974 Solving 13 + x = 12.083045974 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 = 12.083045974 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.083045974 + -13 x = 12.083045974 + -13 Combine like terms: 12.083045974 + -13 = -0.916954026 x = -0.916954026 Simplifying x = -0.916954026Subproblem 2
x + 13 = -12.083045974 Simplifying x + 13 = -12.083045974 Reorder the terms: 13 + x = -12.083045974 Solving 13 + x = -12.083045974 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 = -12.083045974 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.083045974 + -13 x = -12.083045974 + -13 Combine like terms: -12.083045974 + -13 = -25.083045974 x = -25.083045974 Simplifying x = -25.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.916954026, -25.083045974}
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