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Simplifying x2 + -6x + 120 = 180 Reorder the terms: 120 + -6x + x2 = 180 Solving 120 + -6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 120 + -180 + -6x + x2 = 180 + -180 Combine like terms: 120 + -180 = -60 -60 + -6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -60 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -6x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -6x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -6x + x2 = 0 + 60 -6x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -6x + x2 = 60 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 60 + 9 Reorder the terms: 9 + -6x + x2 = 60 + 9 Combine like terms: 60 + 9 = 69 9 + -6x + x2 = 69 Factor a perfect square on the left side: (x + -3)(x + -3) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + -3) equal to 8.306623863 and -8.306623863.Subproblem 1
x + -3 = 8.306623863 Simplifying x + -3 = 8.306623863 Reorder the terms: -3 + x = 8.306623863 Solving -3 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 8.306623863 + 3 Combine like terms: -3 + 3 = 0 0 + x = 8.306623863 + 3 x = 8.306623863 + 3 Combine like terms: 8.306623863 + 3 = 11.306623863 x = 11.306623863 Simplifying x = 11.306623863Subproblem 2
x + -3 = -8.306623863 Simplifying x + -3 = -8.306623863 Reorder the terms: -3 + x = -8.306623863 Solving -3 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -8.306623863 + 3 Combine like terms: -3 + 3 = 0 0 + x = -8.306623863 + 3 x = -8.306623863 + 3 Combine like terms: -8.306623863 + 3 = -5.306623863 x = -5.306623863 Simplifying x = -5.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.306623863, -5.306623863}
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