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Simplifying x2 + -16x + -108 = 0 Reorder the terms: -108 + -16x + x2 = 0 Solving -108 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -16x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -16x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -16x + x2 = 0 + 108 -16x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -16x + x2 = 108 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 = 108 + 64 Reorder the terms: 64 + -16x + x2 = 108 + 64 Combine like terms: 108 + 64 = 172 64 + -16x + x2 = 172 Factor a perfect square on the left side: (x + -8)(x + -8) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + -8) equal to 13.114877049 and -13.114877049.Subproblem 1
x + -8 = 13.114877049 Simplifying x + -8 = 13.114877049 Reorder the terms: -8 + x = 13.114877049 Solving -8 + x = 13.114877049 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 = 13.114877049 + 8 Combine like terms: -8 + 8 = 0 0 + x = 13.114877049 + 8 x = 13.114877049 + 8 Combine like terms: 13.114877049 + 8 = 21.114877049 x = 21.114877049 Simplifying x = 21.114877049Subproblem 2
x + -8 = -13.114877049 Simplifying x + -8 = -13.114877049 Reorder the terms: -8 + x = -13.114877049 Solving -8 + x = -13.114877049 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 = -13.114877049 + 8 Combine like terms: -8 + 8 = 0 0 + x = -13.114877049 + 8 x = -13.114877049 + 8 Combine like terms: -13.114877049 + 8 = -5.114877049 x = -5.114877049 Simplifying x = -5.114877049Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.114877049, -5.114877049}
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