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Simplifying x2 + -12x + -122 = 0 Reorder the terms: -122 + -12x + x2 = 0 Solving -122 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + -12x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + -12x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + -12x + x2 = 0 + 122 -12x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 -12x + x2 = 122 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 = 122 + 36 Reorder the terms: 36 + -12x + x2 = 122 + 36 Combine like terms: 122 + 36 = 158 36 + -12x + x2 = 158 Factor a perfect square on the left side: (x + -6)(x + -6) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (x + -6) equal to 12.56980509 and -12.56980509.Subproblem 1
x + -6 = 12.56980509 Simplifying x + -6 = 12.56980509 Reorder the terms: -6 + x = 12.56980509 Solving -6 + x = 12.56980509 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 = 12.56980509 + 6 Combine like terms: -6 + 6 = 0 0 + x = 12.56980509 + 6 x = 12.56980509 + 6 Combine like terms: 12.56980509 + 6 = 18.56980509 x = 18.56980509 Simplifying x = 18.56980509Subproblem 2
x + -6 = -12.56980509 Simplifying x + -6 = -12.56980509 Reorder the terms: -6 + x = -12.56980509 Solving -6 + x = -12.56980509 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 = -12.56980509 + 6 Combine like terms: -6 + 6 = 0 0 + x = -12.56980509 + 6 x = -12.56980509 + 6 Combine like terms: -12.56980509 + 6 = -6.56980509 x = -6.56980509 Simplifying x = -6.56980509Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.56980509, -6.56980509}
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