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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 = 5.66563146 x = 5.66563146 Simplifying x = 5.66563146Subproblem 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 = -101.66563146 x = -101.66563146 Simplifying x = -101.66563146Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.66563146, -101.66563146}
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