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Simplifying x2 + -22x + 102 = 0 Reorder the terms: 102 + -22x + x2 = 0 Solving 102 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-102' to each side of the equation. 102 + -22x + -102 + x2 = 0 + -102 Reorder the terms: 102 + -102 + -22x + x2 = 0 + -102 Combine like terms: 102 + -102 = 0 0 + -22x + x2 = 0 + -102 -22x + x2 = 0 + -102 Combine like terms: 0 + -102 = -102 -22x + x2 = -102 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 = -102 + 121 Reorder the terms: 121 + -22x + x2 = -102 + 121 Combine like terms: -102 + 121 = 19 121 + -22x + x2 = 19 Factor a perfect square on the left side: (x + -11)(x + -11) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -11) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -11 = 4.358898944 Simplifying x + -11 = 4.358898944 Reorder the terms: -11 + x = 4.358898944 Solving -11 + x = 4.358898944 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 = 4.358898944 + 11 Combine like terms: -11 + 11 = 0 0 + x = 4.358898944 + 11 x = 4.358898944 + 11 Combine like terms: 4.358898944 + 11 = 15.358898944 x = 15.358898944 Simplifying x = 15.358898944Subproblem 2
x + -11 = -4.358898944 Simplifying x + -11 = -4.358898944 Reorder the terms: -11 + x = -4.358898944 Solving -11 + x = -4.358898944 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 = -4.358898944 + 11 Combine like terms: -11 + 11 = 0 0 + x = -4.358898944 + 11 x = -4.358898944 + 11 Combine like terms: -4.358898944 + 11 = 6.641101056 x = 6.641101056 Simplifying x = 6.641101056Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.358898944, 6.641101056}
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