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Simplifying x2 + -48x + -2304 = -2560 Reorder the terms: -2304 + -48x + x2 = -2560 Solving -2304 + -48x + x2 = -2560 Solving for variable 'x'. Reorder the terms: -2304 + 2560 + -48x + x2 = -2560 + 2560 Combine like terms: -2304 + 2560 = 256 256 + -48x + x2 = -2560 + 2560 Combine like terms: -2560 + 2560 = 0 256 + -48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + -48x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + -48x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -48x + x2 = 0 + -256 -48x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 -48x + x2 = -256 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = -256 + 576 Reorder the terms: 576 + -48x + x2 = -256 + 576 Combine like terms: -256 + 576 = 320 576 + -48x + x2 = 320 Factor a perfect square on the left side: (x + -24)(x + -24) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + -24) equal to 17.88854382 and -17.88854382.Subproblem 1
x + -24 = 17.88854382 Simplifying x + -24 = 17.88854382 Reorder the terms: -24 + x = 17.88854382 Solving -24 + x = 17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 17.88854382 + 24 Combine like terms: -24 + 24 = 0 0 + x = 17.88854382 + 24 x = 17.88854382 + 24 Combine like terms: 17.88854382 + 24 = 41.88854382 x = 41.88854382 Simplifying x = 41.88854382Subproblem 2
x + -24 = -17.88854382 Simplifying x + -24 = -17.88854382 Reorder the terms: -24 + x = -17.88854382 Solving -24 + x = -17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -17.88854382 + 24 Combine like terms: -24 + 24 = 0 0 + x = -17.88854382 + 24 x = -17.88854382 + 24 Combine like terms: -17.88854382 + 24 = 6.11145618 x = 6.11145618 Simplifying x = 6.11145618Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.88854382, 6.11145618}
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