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Simplifying x2 + -12x + -116 = 0 Reorder the terms: -116 + -12x + x2 = 0 Solving -116 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + -12x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + -12x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + -12x + x2 = 0 + 116 -12x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 -12x + x2 = 116 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 116 + 36 Reorder the terms: 36 + -12x + x2 = 116 + 36 Combine like terms: 116 + 36 = 152 36 + -12x + x2 = 152 Factor a perfect square on the left side: (x + -6)(x + -6) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (x + -6) equal to 12.328828006 and -12.328828006.Subproblem 1
x + -6 = 12.328828006 Simplifying x + -6 = 12.328828006 Reorder the terms: -6 + x = 12.328828006 Solving -6 + x = 12.328828006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 12.328828006 + 6 Combine like terms: -6 + 6 = 0 0 + x = 12.328828006 + 6 x = 12.328828006 + 6 Combine like terms: 12.328828006 + 6 = 18.328828006 x = 18.328828006 Simplifying x = 18.328828006Subproblem 2
x + -6 = -12.328828006 Simplifying x + -6 = -12.328828006 Reorder the terms: -6 + x = -12.328828006 Solving -6 + x = -12.328828006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -12.328828006 + 6 Combine like terms: -6 + 6 = 0 0 + x = -12.328828006 + 6 x = -12.328828006 + 6 Combine like terms: -12.328828006 + 6 = -6.328828006 x = -6.328828006 Simplifying x = -6.328828006Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.328828006, -6.328828006}
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