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Simplifying x2 + -12x + -180 = 0 Reorder the terms: -180 + -12x + x2 = 0 Solving -180 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -12x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -12x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -12x + x2 = 0 + 180 -12x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -12x + x2 = 180 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 = 180 + 36 Reorder the terms: 36 + -12x + x2 = 180 + 36 Combine like terms: 180 + 36 = 216 36 + -12x + x2 = 216 Factor a perfect square on the left side: (x + -6)(x + -6) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + -6) equal to 14.696938457 and -14.696938457.Subproblem 1
x + -6 = 14.696938457 Simplifying x + -6 = 14.696938457 Reorder the terms: -6 + x = 14.696938457 Solving -6 + x = 14.696938457 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 = 14.696938457 + 6 Combine like terms: -6 + 6 = 0 0 + x = 14.696938457 + 6 x = 14.696938457 + 6 Combine like terms: 14.696938457 + 6 = 20.696938457 x = 20.696938457 Simplifying x = 20.696938457Subproblem 2
x + -6 = -14.696938457 Simplifying x + -6 = -14.696938457 Reorder the terms: -6 + x = -14.696938457 Solving -6 + x = -14.696938457 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 = -14.696938457 + 6 Combine like terms: -6 + 6 = 0 0 + x = -14.696938457 + 6 x = -14.696938457 + 6 Combine like terms: -14.696938457 + 6 = -8.696938457 x = -8.696938457 Simplifying x = -8.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.696938457, -8.696938457}
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