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Simplifying x2 + -96x + -576 = 0 Reorder the terms: -576 + -96x + x2 = 0 Solving -576 + -96x + 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 + -96x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + -96x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + -96x + x2 = 0 + 576 -96x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 -96x + x2 = 576 The x term is -96x. Take half its coefficient (-48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. -96x + 2304 + x2 = 576 + 2304 Reorder the terms: 2304 + -96x + x2 = 576 + 2304 Combine like terms: 576 + 2304 = 2880 2304 + -96x + x2 = 2880 Factor a perfect square on the left side: (x + -48)(x + -48) = 2880 Calculate the square root of the right side: 53.66563146 Break this problem into two subproblems by setting (x + -48) equal to 53.66563146 and -53.66563146.Subproblem 1
x + -48 = 53.66563146 Simplifying x + -48 = 53.66563146 Reorder the terms: -48 + x = 53.66563146 Solving -48 + x = 53.66563146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 53.66563146 + 48 Combine like terms: -48 + 48 = 0 0 + x = 53.66563146 + 48 x = 53.66563146 + 48 Combine like terms: 53.66563146 + 48 = 101.66563146 x = 101.66563146 Simplifying x = 101.66563146Subproblem 2
x + -48 = -53.66563146 Simplifying x + -48 = -53.66563146 Reorder the terms: -48 + x = -53.66563146 Solving -48 + x = -53.66563146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -53.66563146 + 48 Combine like terms: -48 + 48 = 0 0 + x = -53.66563146 + 48 x = -53.66563146 + 48 Combine like terms: -53.66563146 + 48 = -5.66563146 x = -5.66563146 Simplifying x = -5.66563146Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.66563146, -5.66563146}
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