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Simplifying x2 + -22x + -56 = 0 Reorder the terms: -56 + -22x + x2 = 0 Solving -56 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -22x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -22x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -22x + x2 = 0 + 56 -22x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -22x + x2 = 56 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 = 56 + 121 Reorder the terms: 121 + -22x + x2 = 56 + 121 Combine like terms: 56 + 121 = 177 121 + -22x + x2 = 177 Factor a perfect square on the left side: (x + -11)(x + -11) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + -11) equal to 13.304134696 and -13.304134696.Subproblem 1
x + -11 = 13.304134696 Simplifying x + -11 = 13.304134696 Reorder the terms: -11 + x = 13.304134696 Solving -11 + x = 13.304134696 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 = 13.304134696 + 11 Combine like terms: -11 + 11 = 0 0 + x = 13.304134696 + 11 x = 13.304134696 + 11 Combine like terms: 13.304134696 + 11 = 24.304134696 x = 24.304134696 Simplifying x = 24.304134696Subproblem 2
x + -11 = -13.304134696 Simplifying x + -11 = -13.304134696 Reorder the terms: -11 + x = -13.304134696 Solving -11 + x = -13.304134696 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 = -13.304134696 + 11 Combine like terms: -11 + 11 = 0 0 + x = -13.304134696 + 11 x = -13.304134696 + 11 Combine like terms: -13.304134696 + 11 = -2.304134696 x = -2.304134696 Simplifying x = -2.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.304134696, -2.304134696}
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