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Simplifying x2 + 22x + 59 = 0 Reorder the terms: 59 + 22x + x2 = 0 Solving 59 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 22x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 22x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 22x + x2 = 0 + -59 22x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 22x + x2 = -59 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 = -59 + 121 Reorder the terms: 121 + 22x + x2 = -59 + 121 Combine like terms: -59 + 121 = 62 121 + 22x + x2 = 62 Factor a perfect square on the left side: (x + 11)(x + 11) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + 11) equal to 7.874007874 and -7.874007874.Subproblem 1
x + 11 = 7.874007874 Simplifying x + 11 = 7.874007874 Reorder the terms: 11 + x = 7.874007874 Solving 11 + x = 7.874007874 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 = 7.874007874 + -11 Combine like terms: 11 + -11 = 0 0 + x = 7.874007874 + -11 x = 7.874007874 + -11 Combine like terms: 7.874007874 + -11 = -3.125992126 x = -3.125992126 Simplifying x = -3.125992126Subproblem 2
x + 11 = -7.874007874 Simplifying x + 11 = -7.874007874 Reorder the terms: 11 + x = -7.874007874 Solving 11 + x = -7.874007874 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 = -7.874007874 + -11 Combine like terms: 11 + -11 = 0 0 + x = -7.874007874 + -11 x = -7.874007874 + -11 Combine like terms: -7.874007874 + -11 = -18.874007874 x = -18.874007874 Simplifying x = -18.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.125992126, -18.874007874}
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