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Simplifying x2 + 22x = 0 + -102 Reorder the terms: 22x + x2 = 0 + -102 Combine like terms: 0 + -102 = -102 22x + x2 = -102 Solving 22x + x2 = -102 Solving for variable 'x'. Reorder the terms: 102 + 22x + x2 = -102 + 102 Combine like terms: -102 + 102 = 0 102 + 22x + x2 = 0 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 = -6.641101056 x = -6.641101056 Simplifying x = -6.641101056Subproblem 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 = -15.358898944 x = -15.358898944 Simplifying x = -15.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.641101056, -15.358898944}
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