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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 = 65 121 + -22x + x2 = 65 Factor a perfect square on the left side: (x + -11)(x + -11) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -11) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -11 = 8.062257748 Simplifying x + -11 = 8.062257748 Reorder the terms: -11 + x = 8.062257748 Solving -11 + x = 8.062257748 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 = 8.062257748 + 11 Combine like terms: -11 + 11 = 0 0 + x = 8.062257748 + 11 x = 8.062257748 + 11 Combine like terms: 8.062257748 + 11 = 19.062257748 x = 19.062257748 Simplifying x = 19.062257748Subproblem 2
x + -11 = -8.062257748 Simplifying x + -11 = -8.062257748 Reorder the terms: -11 + x = -8.062257748 Solving -11 + x = -8.062257748 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 = -8.062257748 + 11 Combine like terms: -11 + 11 = 0 0 + x = -8.062257748 + 11 x = -8.062257748 + 11 Combine like terms: -8.062257748 + 11 = 2.937742252 x = 2.937742252 Simplifying x = 2.937742252Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.062257748, 2.937742252}
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