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Simplifying x2 + -8x + -109 = 0 Reorder the terms: -109 + -8x + x2 = 0 Solving -109 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '109' to each side of the equation. -109 + -8x + 109 + x2 = 0 + 109 Reorder the terms: -109 + 109 + -8x + x2 = 0 + 109 Combine like terms: -109 + 109 = 0 0 + -8x + x2 = 0 + 109 -8x + x2 = 0 + 109 Combine like terms: 0 + 109 = 109 -8x + x2 = 109 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 = 109 + 16 Reorder the terms: 16 + -8x + x2 = 109 + 16 Combine like terms: 109 + 16 = 125 16 + -8x + x2 = 125 Factor a perfect square on the left side: (x + -4)(x + -4) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + -4) equal to 11.180339887 and -11.180339887.Subproblem 1
x + -4 = 11.180339887 Simplifying x + -4 = 11.180339887 Reorder the terms: -4 + x = 11.180339887 Solving -4 + x = 11.180339887 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 = 11.180339887 + 4 Combine like terms: -4 + 4 = 0 0 + x = 11.180339887 + 4 x = 11.180339887 + 4 Combine like terms: 11.180339887 + 4 = 15.180339887 x = 15.180339887 Simplifying x = 15.180339887Subproblem 2
x + -4 = -11.180339887 Simplifying x + -4 = -11.180339887 Reorder the terms: -4 + x = -11.180339887 Solving -4 + x = -11.180339887 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 = -11.180339887 + 4 Combine like terms: -4 + 4 = 0 0 + x = -11.180339887 + 4 x = -11.180339887 + 4 Combine like terms: -11.180339887 + 4 = -7.180339887 x = -7.180339887 Simplifying x = -7.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.180339887, -7.180339887}
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