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Simplifying x2 + -22x + -40 = 0 Reorder the terms: -40 + -22x + x2 = 0 Solving -40 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -22x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -22x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -22x + x2 = 0 + 40 -22x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -22x + x2 = 40 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 40 + 121 Reorder the terms: 121 + -22x + x2 = 40 + 121 Combine like terms: 40 + 121 = 161 121 + -22x + x2 = 161 Factor a perfect square on the left side: (x + -11)(x + -11) = 161 Calculate the square root of the right side: 12.68857754 Break this problem into two subproblems by setting (x + -11) equal to 12.68857754 and -12.68857754.Subproblem 1
x + -11 = 12.68857754 Simplifying x + -11 = 12.68857754 Reorder the terms: -11 + x = 12.68857754 Solving -11 + x = 12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 12.68857754 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.68857754 + 11 x = 12.68857754 + 11 Combine like terms: 12.68857754 + 11 = 23.68857754 x = 23.68857754 Simplifying x = 23.68857754Subproblem 2
x + -11 = -12.68857754 Simplifying x + -11 = -12.68857754 Reorder the terms: -11 + x = -12.68857754 Solving -11 + x = -12.68857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -12.68857754 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.68857754 + 11 x = -12.68857754 + 11 Combine like terms: -12.68857754 + 11 = -1.68857754 x = -1.68857754 Simplifying x = -1.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.68857754, -1.68857754}
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