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Simplifying (x * x) + -20x + -100 = 68 Multiply x * x (x2) + -20x + -100 = 68 x2 + -20x + -100 = 68 Reorder the terms: -100 + -20x + x2 = 68 Solving -100 + -20x + x2 = 68 Solving for variable 'x'. Reorder the terms: -100 + -68 + -20x + x2 = 68 + -68 Combine like terms: -100 + -68 = -168 -168 + -20x + x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -168 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '168' to each side of the equation. -168 + -20x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + -20x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -20x + x2 = 0 + 168 -20x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 -20x + x2 = 168 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 168 + 100 Reorder the terms: 100 + -20x + x2 = 168 + 100 Combine like terms: 168 + 100 = 268 100 + -20x + x2 = 268 Factor a perfect square on the left side: (x + -10)(x + -10) = 268 Calculate the square root of the right side: 16.370705544 Break this problem into two subproblems by setting (x + -10) equal to 16.370705544 and -16.370705544.Subproblem 1
x + -10 = 16.370705544 Simplifying x + -10 = 16.370705544 Reorder the terms: -10 + x = 16.370705544 Solving -10 + x = 16.370705544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 16.370705544 + 10 Combine like terms: -10 + 10 = 0 0 + x = 16.370705544 + 10 x = 16.370705544 + 10 Combine like terms: 16.370705544 + 10 = 26.370705544 x = 26.370705544 Simplifying x = 26.370705544Subproblem 2
x + -10 = -16.370705544 Simplifying x + -10 = -16.370705544 Reorder the terms: -10 + x = -16.370705544 Solving -10 + x = -16.370705544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -16.370705544 + 10 Combine like terms: -10 + 10 = 0 0 + x = -16.370705544 + 10 x = -16.370705544 + 10 Combine like terms: -16.370705544 + 10 = -6.370705544 x = -6.370705544 Simplifying x = -6.370705544Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.370705544, -6.370705544}
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