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Simplifying x2 + -15x + -120 = 0 Reorder the terms: -120 + -15x + x2 = 0 Solving -120 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -15x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -15x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -15x + x2 = 0 + 120 -15x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -15x + x2 = 120 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 120 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 120 + 56.25 Combine like terms: 120 + 56.25 = 176.25 56.25 + -15x + x2 = 176.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (x + -7.5) equal to 13.275918047 and -13.275918047.Subproblem 1
x + -7.5 = 13.275918047 Simplifying x + -7.5 = 13.275918047 Reorder the terms: -7.5 + x = 13.275918047 Solving -7.5 + x = 13.275918047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 13.275918047 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 13.275918047 + 7.5 x = 13.275918047 + 7.5 Combine like terms: 13.275918047 + 7.5 = 20.775918047 x = 20.775918047 Simplifying x = 20.775918047Subproblem 2
x + -7.5 = -13.275918047 Simplifying x + -7.5 = -13.275918047 Reorder the terms: -7.5 + x = -13.275918047 Solving -7.5 + x = -13.275918047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -13.275918047 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -13.275918047 + 7.5 x = -13.275918047 + 7.5 Combine like terms: -13.275918047 + 7.5 = -5.775918047 x = -5.775918047 Simplifying x = -5.775918047Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.775918047, -5.775918047}
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