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Simplifying x2 + -22x + 58 = 0 Reorder the terms: 58 + -22x + x2 = 0 Solving 58 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -22x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -22x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -22x + x2 = 0 + -58 -22x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -22x + x2 = -58 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 = -58 + 121 Reorder the terms: 121 + -22x + x2 = -58 + 121 Combine like terms: -58 + 121 = 63 121 + -22x + x2 = 63 Factor a perfect square on the left side: (x + -11)(x + -11) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -11) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -11 = 7.937253933 Simplifying x + -11 = 7.937253933 Reorder the terms: -11 + x = 7.937253933 Solving -11 + x = 7.937253933 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 = 7.937253933 + 11 Combine like terms: -11 + 11 = 0 0 + x = 7.937253933 + 11 x = 7.937253933 + 11 Combine like terms: 7.937253933 + 11 = 18.937253933 x = 18.937253933 Simplifying x = 18.937253933Subproblem 2
x + -11 = -7.937253933 Simplifying x + -11 = -7.937253933 Reorder the terms: -11 + x = -7.937253933 Solving -11 + x = -7.937253933 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 = -7.937253933 + 11 Combine like terms: -11 + 11 = 0 0 + x = -7.937253933 + 11 x = -7.937253933 + 11 Combine like terms: -7.937253933 + 11 = 3.062746067 x = 3.062746067 Simplifying x = 3.062746067Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.937253933, 3.062746067}
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