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Simplifying x2 + 26x + 12 = 0 Reorder the terms: 12 + 26x + x2 = 0 Solving 12 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 26x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 26x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 26x + x2 = 0 + -12 26x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 26x + x2 = -12 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 = -12 + 169 Reorder the terms: 169 + 26x + x2 = -12 + 169 Combine like terms: -12 + 169 = 157 169 + 26x + x2 = 157 Factor a perfect square on the left side: (x + 13)(x + 13) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 13) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 13 = 12.529964086 Simplifying x + 13 = 12.529964086 Reorder the terms: 13 + x = 12.529964086 Solving 13 + x = 12.529964086 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 = 12.529964086 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.529964086 + -13 x = 12.529964086 + -13 Combine like terms: 12.529964086 + -13 = -0.470035914 x = -0.470035914 Simplifying x = -0.470035914Subproblem 2
x + 13 = -12.529964086 Simplifying x + 13 = -12.529964086 Reorder the terms: 13 + x = -12.529964086 Solving 13 + x = -12.529964086 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 = -12.529964086 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.529964086 + -13 x = -12.529964086 + -13 Combine like terms: -12.529964086 + -13 = -25.529964086 x = -25.529964086 Simplifying x = -25.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.470035914, -25.529964086}
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