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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 = 1.68857754 x = 1.68857754 Simplifying x = 1.68857754Subproblem 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 = -23.68857754 x = -23.68857754 Simplifying x = -23.68857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.68857754, -23.68857754}
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