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Simplifying x2 + 6x + -360 = 0 Reorder the terms: -360 + 6x + x2 = 0 Solving -360 + 6x + 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 + 6x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 6x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 6x + x2 = 0 + 360 6x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 6x + x2 = 360 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 = 360 + 9 Reorder the terms: 9 + 6x + x2 = 360 + 9 Combine like terms: 360 + 9 = 369 9 + 6x + x2 = 369 Factor a perfect square on the left side: (x + 3)(x + 3) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + 3) equal to 19.209372712 and -19.209372712.Subproblem 1
x + 3 = 19.209372712 Simplifying x + 3 = 19.209372712 Reorder the terms: 3 + x = 19.209372712 Solving 3 + x = 19.209372712 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 = 19.209372712 + -3 Combine like terms: 3 + -3 = 0 0 + x = 19.209372712 + -3 x = 19.209372712 + -3 Combine like terms: 19.209372712 + -3 = 16.209372712 x = 16.209372712 Simplifying x = 16.209372712Subproblem 2
x + 3 = -19.209372712 Simplifying x + 3 = -19.209372712 Reorder the terms: 3 + x = -19.209372712 Solving 3 + x = -19.209372712 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 = -19.209372712 + -3 Combine like terms: 3 + -3 = 0 0 + x = -19.209372712 + -3 x = -19.209372712 + -3 Combine like terms: -19.209372712 + -3 = -22.209372712 x = -22.209372712 Simplifying x = -22.209372712Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.209372712, -22.209372712}
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