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Simplifying x2 + -44x + 100 = 8 Reorder the terms: 100 + -44x + x2 = 8 Solving 100 + -44x + x2 = 8 Solving for variable 'x'. Reorder the terms: 100 + -8 + -44x + x2 = 8 + -8 Combine like terms: 100 + -8 = 92 92 + -44x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 92 + -44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-92' to each side of the equation. 92 + -44x + -92 + x2 = 0 + -92 Reorder the terms: 92 + -92 + -44x + x2 = 0 + -92 Combine like terms: 92 + -92 = 0 0 + -44x + x2 = 0 + -92 -44x + x2 = 0 + -92 Combine like terms: 0 + -92 = -92 -44x + x2 = -92 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -92 + 484 Reorder the terms: 484 + -44x + x2 = -92 + 484 Combine like terms: -92 + 484 = 392 484 + -44x + x2 = 392 Factor a perfect square on the left side: (x + -22)(x + -22) = 392 Calculate the square root of the right side: 19.798989873 Break this problem into two subproblems by setting (x + -22) equal to 19.798989873 and -19.798989873.Subproblem 1
x + -22 = 19.798989873 Simplifying x + -22 = 19.798989873 Reorder the terms: -22 + x = 19.798989873 Solving -22 + x = 19.798989873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 19.798989873 + 22 Combine like terms: -22 + 22 = 0 0 + x = 19.798989873 + 22 x = 19.798989873 + 22 Combine like terms: 19.798989873 + 22 = 41.798989873 x = 41.798989873 Simplifying x = 41.798989873Subproblem 2
x + -22 = -19.798989873 Simplifying x + -22 = -19.798989873 Reorder the terms: -22 + x = -19.798989873 Solving -22 + x = -19.798989873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -19.798989873 + 22 Combine like terms: -22 + 22 = 0 0 + x = -19.798989873 + 22 x = -19.798989873 + 22 Combine like terms: -19.798989873 + 22 = 2.201010127 x = 2.201010127 Simplifying x = 2.201010127Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.798989873, 2.201010127}
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