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Simplifying x2 + 16x + -360 = 0 Reorder the terms: -360 + 16x + x2 = 0 Solving -360 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 16x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 16x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 16x + x2 = 0 + 360 16x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 16x + x2 = 360 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 360 + 64 Reorder the terms: 64 + 16x + x2 = 360 + 64 Combine like terms: 360 + 64 = 424 64 + 16x + x2 = 424 Factor a perfect square on the left side: (x + 8)(x + 8) = 424 Calculate the square root of the right side: 20.591260282 Break this problem into two subproblems by setting (x + 8) equal to 20.591260282 and -20.591260282.Subproblem 1
x + 8 = 20.591260282 Simplifying x + 8 = 20.591260282 Reorder the terms: 8 + x = 20.591260282 Solving 8 + x = 20.591260282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 20.591260282 + -8 Combine like terms: 8 + -8 = 0 0 + x = 20.591260282 + -8 x = 20.591260282 + -8 Combine like terms: 20.591260282 + -8 = 12.591260282 x = 12.591260282 Simplifying x = 12.591260282Subproblem 2
x + 8 = -20.591260282 Simplifying x + 8 = -20.591260282 Reorder the terms: 8 + x = -20.591260282 Solving 8 + x = -20.591260282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -20.591260282 + -8 Combine like terms: 8 + -8 = 0 0 + x = -20.591260282 + -8 x = -20.591260282 + -8 Combine like terms: -20.591260282 + -8 = -28.591260282 x = -28.591260282 Simplifying x = -28.591260282Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.591260282, -28.591260282}
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