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Simplifying x2 + 26x + 37 = 0 Reorder the terms: 37 + 26x + x2 = 0 Solving 37 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 26x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 26x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 26x + x2 = 0 + -37 26x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 26x + x2 = -37 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 = -37 + 169 Reorder the terms: 169 + 26x + x2 = -37 + 169 Combine like terms: -37 + 169 = 132 169 + 26x + x2 = 132 Factor a perfect square on the left side: (x + 13)(x + 13) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + 13) equal to 11.489125293 and -11.489125293.Subproblem 1
x + 13 = 11.489125293 Simplifying x + 13 = 11.489125293 Reorder the terms: 13 + x = 11.489125293 Solving 13 + x = 11.489125293 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 = 11.489125293 + -13 Combine like terms: 13 + -13 = 0 0 + x = 11.489125293 + -13 x = 11.489125293 + -13 Combine like terms: 11.489125293 + -13 = -1.510874707 x = -1.510874707 Simplifying x = -1.510874707Subproblem 2
x + 13 = -11.489125293 Simplifying x + 13 = -11.489125293 Reorder the terms: 13 + x = -11.489125293 Solving 13 + x = -11.489125293 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 = -11.489125293 + -13 Combine like terms: 13 + -13 = 0 0 + x = -11.489125293 + -13 x = -11.489125293 + -13 Combine like terms: -11.489125293 + -13 = -24.489125293 x = -24.489125293 Simplifying x = -24.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.510874707, -24.489125293}
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