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Simplifying x2 + -24x + -16 = 180 Reorder the terms: -16 + -24x + x2 = 180 Solving -16 + -24x + x2 = 180 Solving for variable 'x'. Reorder the terms: -16 + -180 + -24x + x2 = 180 + -180 Combine like terms: -16 + -180 = -196 -196 + -24x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -196 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '196' to each side of the equation. -196 + -24x + 196 + x2 = 0 + 196 Reorder the terms: -196 + 196 + -24x + x2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + -24x + x2 = 0 + 196 -24x + x2 = 0 + 196 Combine like terms: 0 + 196 = 196 -24x + x2 = 196 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 = 196 + 144 Reorder the terms: 144 + -24x + x2 = 196 + 144 Combine like terms: 196 + 144 = 340 144 + -24x + x2 = 340 Factor a perfect square on the left side: (x + -12)(x + -12) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (x + -12) equal to 18.439088915 and -18.439088915.Subproblem 1
x + -12 = 18.439088915 Simplifying x + -12 = 18.439088915 Reorder the terms: -12 + x = 18.439088915 Solving -12 + x = 18.439088915 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 = 18.439088915 + 12 Combine like terms: -12 + 12 = 0 0 + x = 18.439088915 + 12 x = 18.439088915 + 12 Combine like terms: 18.439088915 + 12 = 30.439088915 x = 30.439088915 Simplifying x = 30.439088915Subproblem 2
x + -12 = -18.439088915 Simplifying x + -12 = -18.439088915 Reorder the terms: -12 + x = -18.439088915 Solving -12 + x = -18.439088915 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 = -18.439088915 + 12 Combine like terms: -12 + 12 = 0 0 + x = -18.439088915 + 12 x = -18.439088915 + 12 Combine like terms: -18.439088915 + 12 = -6.439088915 x = -6.439088915 Simplifying x = -6.439088915Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.439088915, -6.439088915}
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