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Simplifying x2 + 48x + -576 = 0 Reorder the terms: -576 + 48x + x2 = 0 Solving -576 + 48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 48x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + 48x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 48x + x2 = 0 + 576 48x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 48x + x2 = 576 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 = 576 + 576 Reorder the terms: 576 + 48x + x2 = 576 + 576 Combine like terms: 576 + 576 = 1152 576 + 48x + x2 = 1152 Factor a perfect square on the left side: (x + 24)(x + 24) = 1152 Calculate the square root of the right side: 33.941125497 Break this problem into two subproblems by setting (x + 24) equal to 33.941125497 and -33.941125497.Subproblem 1
x + 24 = 33.941125497 Simplifying x + 24 = 33.941125497 Reorder the terms: 24 + x = 33.941125497 Solving 24 + x = 33.941125497 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 = 33.941125497 + -24 Combine like terms: 24 + -24 = 0 0 + x = 33.941125497 + -24 x = 33.941125497 + -24 Combine like terms: 33.941125497 + -24 = 9.941125497 x = 9.941125497 Simplifying x = 9.941125497Subproblem 2
x + 24 = -33.941125497 Simplifying x + 24 = -33.941125497 Reorder the terms: 24 + x = -33.941125497 Solving 24 + x = -33.941125497 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 = -33.941125497 + -24 Combine like terms: 24 + -24 = 0 0 + x = -33.941125497 + -24 x = -33.941125497 + -24 Combine like terms: -33.941125497 + -24 = -57.941125497 x = -57.941125497 Simplifying x = -57.941125497Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.941125497, -57.941125497}
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