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Simplifying x2 + -8x + -107 = 0 Reorder the terms: -107 + -8x + x2 = 0 Solving -107 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '107' to each side of the equation. -107 + -8x + 107 + x2 = 0 + 107 Reorder the terms: -107 + 107 + -8x + x2 = 0 + 107 Combine like terms: -107 + 107 = 0 0 + -8x + x2 = 0 + 107 -8x + x2 = 0 + 107 Combine like terms: 0 + 107 = 107 -8x + x2 = 107 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 107 + 16 Reorder the terms: 16 + -8x + x2 = 107 + 16 Combine like terms: 107 + 16 = 123 16 + -8x + x2 = 123 Factor a perfect square on the left side: (x + -4)(x + -4) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + -4) equal to 11.090536506 and -11.090536506.Subproblem 1
x + -4 = 11.090536506 Simplifying x + -4 = 11.090536506 Reorder the terms: -4 + x = 11.090536506 Solving -4 + x = 11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 11.090536506 + 4 Combine like terms: -4 + 4 = 0 0 + x = 11.090536506 + 4 x = 11.090536506 + 4 Combine like terms: 11.090536506 + 4 = 15.090536506 x = 15.090536506 Simplifying x = 15.090536506Subproblem 2
x + -4 = -11.090536506 Simplifying x + -4 = -11.090536506 Reorder the terms: -4 + x = -11.090536506 Solving -4 + x = -11.090536506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -11.090536506 + 4 Combine like terms: -4 + 4 = 0 0 + x = -11.090536506 + 4 x = -11.090536506 + 4 Combine like terms: -11.090536506 + 4 = -7.090536506 x = -7.090536506 Simplifying x = -7.090536506Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.090536506, -7.090536506}
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