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Simplifying x2 + -20x + 92 = 0 Reorder the terms: 92 + -20x + x2 = 0 Solving 92 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-92' to each side of the equation. 92 + -20x + -92 + x2 = 0 + -92 Reorder the terms: 92 + -92 + -20x + x2 = 0 + -92 Combine like terms: 92 + -92 = 0 0 + -20x + x2 = 0 + -92 -20x + x2 = 0 + -92 Combine like terms: 0 + -92 = -92 -20x + x2 = -92 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 = -92 + 100 Reorder the terms: 100 + -20x + x2 = -92 + 100 Combine like terms: -92 + 100 = 8 100 + -20x + x2 = 8 Factor a perfect square on the left side: (x + -10)(x + -10) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -10) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -10 = 2.828427125 Simplifying x + -10 = 2.828427125 Reorder the terms: -10 + x = 2.828427125 Solving -10 + x = 2.828427125 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 = 2.828427125 + 10 Combine like terms: -10 + 10 = 0 0 + x = 2.828427125 + 10 x = 2.828427125 + 10 Combine like terms: 2.828427125 + 10 = 12.828427125 x = 12.828427125 Simplifying x = 12.828427125Subproblem 2
x + -10 = -2.828427125 Simplifying x + -10 = -2.828427125 Reorder the terms: -10 + x = -2.828427125 Solving -10 + x = -2.828427125 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 = -2.828427125 + 10 Combine like terms: -10 + 10 = 0 0 + x = -2.828427125 + 10 x = -2.828427125 + 10 Combine like terms: -2.828427125 + 10 = 7.171572875 x = 7.171572875 Simplifying x = 7.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.828427125, 7.171572875}
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