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Simplifying x2 + -26x + -36 = 0 Reorder the terms: -36 + -26x + x2 = 0 Solving -36 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -26x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -26x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -26x + x2 = 0 + 36 -26x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -26x + x2 = 36 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 = 36 + 169 Reorder the terms: 169 + -26x + x2 = 36 + 169 Combine like terms: 36 + 169 = 205 169 + -26x + x2 = 205 Factor a perfect square on the left side: (x + -13)(x + -13) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + -13) equal to 14.317821063 and -14.317821063.Subproblem 1
x + -13 = 14.317821063 Simplifying x + -13 = 14.317821063 Reorder the terms: -13 + x = 14.317821063 Solving -13 + x = 14.317821063 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 = 14.317821063 + 13 Combine like terms: -13 + 13 = 0 0 + x = 14.317821063 + 13 x = 14.317821063 + 13 Combine like terms: 14.317821063 + 13 = 27.317821063 x = 27.317821063 Simplifying x = 27.317821063Subproblem 2
x + -13 = -14.317821063 Simplifying x + -13 = -14.317821063 Reorder the terms: -13 + x = -14.317821063 Solving -13 + x = -14.317821063 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 = -14.317821063 + 13 Combine like terms: -13 + 13 = 0 0 + x = -14.317821063 + 13 x = -14.317821063 + 13 Combine like terms: -14.317821063 + 13 = -1.317821063 x = -1.317821063 Simplifying x = -1.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.317821063, -1.317821063}
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