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Simplifying x2 + -4x + -360 = 0 Reorder the terms: -360 + -4x + x2 = 0 Solving -360 + -4x + 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 + -4x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -4x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -4x + x2 = 0 + 360 -4x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -4x + x2 = 360 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 360 + 4 Reorder the terms: 4 + -4x + x2 = 360 + 4 Combine like terms: 360 + 4 = 364 4 + -4x + x2 = 364 Factor a perfect square on the left side: (x + -2)(x + -2) = 364 Calculate the square root of the right side: 19.078784028 Break this problem into two subproblems by setting (x + -2) equal to 19.078784028 and -19.078784028.Subproblem 1
x + -2 = 19.078784028 Simplifying x + -2 = 19.078784028 Reorder the terms: -2 + x = 19.078784028 Solving -2 + x = 19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 19.078784028 + 2 Combine like terms: -2 + 2 = 0 0 + x = 19.078784028 + 2 x = 19.078784028 + 2 Combine like terms: 19.078784028 + 2 = 21.078784028 x = 21.078784028 Simplifying x = 21.078784028Subproblem 2
x + -2 = -19.078784028 Simplifying x + -2 = -19.078784028 Reorder the terms: -2 + x = -19.078784028 Solving -2 + x = -19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -19.078784028 + 2 Combine like terms: -2 + 2 = 0 0 + x = -19.078784028 + 2 x = -19.078784028 + 2 Combine like terms: -19.078784028 + 2 = -17.078784028 x = -17.078784028 Simplifying x = -17.078784028Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.078784028, -17.078784028}
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