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Simplifying x2 + -36x + -113 = 0 Reorder the terms: -113 + -36x + x2 = 0 Solving -113 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '113' to each side of the equation. -113 + -36x + 113 + x2 = 0 + 113 Reorder the terms: -113 + 113 + -36x + x2 = 0 + 113 Combine like terms: -113 + 113 = 0 0 + -36x + x2 = 0 + 113 -36x + x2 = 0 + 113 Combine like terms: 0 + 113 = 113 -36x + x2 = 113 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = 113 + 324 Reorder the terms: 324 + -36x + x2 = 113 + 324 Combine like terms: 113 + 324 = 437 324 + -36x + x2 = 437 Factor a perfect square on the left side: (x + -18)(x + -18) = 437 Calculate the square root of the right side: 20.90454496 Break this problem into two subproblems by setting (x + -18) equal to 20.90454496 and -20.90454496.Subproblem 1
x + -18 = 20.90454496 Simplifying x + -18 = 20.90454496 Reorder the terms: -18 + x = 20.90454496 Solving -18 + x = 20.90454496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 20.90454496 + 18 Combine like terms: -18 + 18 = 0 0 + x = 20.90454496 + 18 x = 20.90454496 + 18 Combine like terms: 20.90454496 + 18 = 38.90454496 x = 38.90454496 Simplifying x = 38.90454496Subproblem 2
x + -18 = -20.90454496 Simplifying x + -18 = -20.90454496 Reorder the terms: -18 + x = -20.90454496 Solving -18 + x = -20.90454496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -20.90454496 + 18 Combine like terms: -18 + 18 = 0 0 + x = -20.90454496 + 18 x = -20.90454496 + 18 Combine like terms: -20.90454496 + 18 = -2.90454496 x = -2.90454496 Simplifying x = -2.90454496Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.90454496, -2.90454496}
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