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Simplifying x2 + -8x = 360 Reorder the terms: -8x + x2 = 360 Solving -8x + x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + -8x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + -8x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + -8x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + -8x + x2 = 0 + 360 -8x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 -8x + x2 = 360 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 360 + 16 Reorder the terms: 16 + -8x + x2 = 360 + 16 Combine like terms: 360 + 16 = 376 16 + -8x + x2 = 376 Factor a perfect square on the left side: (x + -4)(x + -4) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + -4) equal to 19.39071943 and -19.39071943.Subproblem 1
x + -4 = 19.39071943 Simplifying x + -4 = 19.39071943 Reorder the terms: -4 + x = 19.39071943 Solving -4 + x = 19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 19.39071943 + 4 Combine like terms: -4 + 4 = 0 0 + x = 19.39071943 + 4 x = 19.39071943 + 4 Combine like terms: 19.39071943 + 4 = 23.39071943 x = 23.39071943 Simplifying x = 23.39071943Subproblem 2
x + -4 = -19.39071943 Simplifying x + -4 = -19.39071943 Reorder the terms: -4 + x = -19.39071943 Solving -4 + x = -19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -19.39071943 + 4 Combine like terms: -4 + 4 = 0 0 + x = -19.39071943 + 4 x = -19.39071943 + 4 Combine like terms: -19.39071943 + 4 = -15.39071943 x = -15.39071943 Simplifying x = -15.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.39071943, -15.39071943}
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