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Simplifying x2 + -16x + -86 = 0 Reorder the terms: -86 + -16x + x2 = 0 Solving -86 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + -16x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + -16x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + -16x + x2 = 0 + 86 -16x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 -16x + x2 = 86 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 86 + 64 Reorder the terms: 64 + -16x + x2 = 86 + 64 Combine like terms: 86 + 64 = 150 64 + -16x + x2 = 150 Factor a perfect square on the left side: (x + -8)(x + -8) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + -8) equal to 12.247448714 and -12.247448714.Subproblem 1
x + -8 = 12.247448714 Simplifying x + -8 = 12.247448714 Reorder the terms: -8 + x = 12.247448714 Solving -8 + x = 12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 12.247448714 + 8 Combine like terms: -8 + 8 = 0 0 + x = 12.247448714 + 8 x = 12.247448714 + 8 Combine like terms: 12.247448714 + 8 = 20.247448714 x = 20.247448714 Simplifying x = 20.247448714Subproblem 2
x + -8 = -12.247448714 Simplifying x + -8 = -12.247448714 Reorder the terms: -8 + x = -12.247448714 Solving -8 + x = -12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -12.247448714 + 8 Combine like terms: -8 + 8 = 0 0 + x = -12.247448714 + 8 x = -12.247448714 + 8 Combine like terms: -12.247448714 + 8 = -4.247448714 x = -4.247448714 Simplifying x = -4.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.247448714, -4.247448714}
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