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Simplifying x2 + -24x + -12 = 180 Reorder the terms: -12 + -24x + x2 = 180 Solving -12 + -24x + x2 = 180 Solving for variable 'x'. Reorder the terms: -12 + -180 + -24x + x2 = 180 + -180 Combine like terms: -12 + -180 = -192 -192 + -24x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -192 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + -24x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + -24x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -24x + x2 = 0 + 192 -24x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 -24x + x2 = 192 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 192 + 144 Reorder the terms: 144 + -24x + x2 = 192 + 144 Combine like terms: 192 + 144 = 336 144 + -24x + x2 = 336 Factor a perfect square on the left side: (x + -12)(x + -12) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + -12) equal to 18.33030278 and -18.33030278.Subproblem 1
x + -12 = 18.33030278 Simplifying x + -12 = 18.33030278 Reorder the terms: -12 + x = 18.33030278 Solving -12 + x = 18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 18.33030278 + 12 Combine like terms: -12 + 12 = 0 0 + x = 18.33030278 + 12 x = 18.33030278 + 12 Combine like terms: 18.33030278 + 12 = 30.33030278 x = 30.33030278 Simplifying x = 30.33030278Subproblem 2
x + -12 = -18.33030278 Simplifying x + -12 = -18.33030278 Reorder the terms: -12 + x = -18.33030278 Solving -12 + x = -18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -18.33030278 + 12 Combine like terms: -12 + 12 = 0 0 + x = -18.33030278 + 12 x = -18.33030278 + 12 Combine like terms: -18.33030278 + 12 = -6.33030278 x = -6.33030278 Simplifying x = -6.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.33030278, -6.33030278}
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