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Simplifying x2 + -8x + -3840 = 0 Reorder the terms: -3840 + -8x + x2 = 0 Solving -3840 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3840' to each side of the equation. -3840 + -8x + 3840 + x2 = 0 + 3840 Reorder the terms: -3840 + 3840 + -8x + x2 = 0 + 3840 Combine like terms: -3840 + 3840 = 0 0 + -8x + x2 = 0 + 3840 -8x + x2 = 0 + 3840 Combine like terms: 0 + 3840 = 3840 -8x + x2 = 3840 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 = 3840 + 16 Reorder the terms: 16 + -8x + x2 = 3840 + 16 Combine like terms: 3840 + 16 = 3856 16 + -8x + x2 = 3856 Factor a perfect square on the left side: (x + -4)(x + -4) = 3856 Calculate the square root of the right side: 62.096698785 Break this problem into two subproblems by setting (x + -4) equal to 62.096698785 and -62.096698785.Subproblem 1
x + -4 = 62.096698785 Simplifying x + -4 = 62.096698785 Reorder the terms: -4 + x = 62.096698785 Solving -4 + x = 62.096698785 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 = 62.096698785 + 4 Combine like terms: -4 + 4 = 0 0 + x = 62.096698785 + 4 x = 62.096698785 + 4 Combine like terms: 62.096698785 + 4 = 66.096698785 x = 66.096698785 Simplifying x = 66.096698785Subproblem 2
x + -4 = -62.096698785 Simplifying x + -4 = -62.096698785 Reorder the terms: -4 + x = -62.096698785 Solving -4 + x = -62.096698785 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 = -62.096698785 + 4 Combine like terms: -4 + 4 = 0 0 + x = -62.096698785 + 4 x = -62.096698785 + 4 Combine like terms: -62.096698785 + 4 = -58.096698785 x = -58.096698785 Simplifying x = -58.096698785Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.096698785, -58.096698785}
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