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Simplifying x2 + 96x + 256 = 0 Reorder the terms: 256 + 96x + x2 = 0 Solving 256 + 96x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + 96x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + 96x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + 96x + x2 = 0 + -256 96x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 96x + x2 = -256 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 = -256 + 2304 Reorder the terms: 2304 + 96x + x2 = -256 + 2304 Combine like terms: -256 + 2304 = 2048 2304 + 96x + x2 = 2048 Factor a perfect square on the left side: (x + 48)(x + 48) = 2048 Calculate the square root of the right side: 45.254833996 Break this problem into two subproblems by setting (x + 48) equal to 45.254833996 and -45.254833996.Subproblem 1
x + 48 = 45.254833996 Simplifying x + 48 = 45.254833996 Reorder the terms: 48 + x = 45.254833996 Solving 48 + x = 45.254833996 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 = 45.254833996 + -48 Combine like terms: 48 + -48 = 0 0 + x = 45.254833996 + -48 x = 45.254833996 + -48 Combine like terms: 45.254833996 + -48 = -2.745166004 x = -2.745166004 Simplifying x = -2.745166004Subproblem 2
x + 48 = -45.254833996 Simplifying x + 48 = -45.254833996 Reorder the terms: 48 + x = -45.254833996 Solving 48 + x = -45.254833996 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 = -45.254833996 + -48 Combine like terms: 48 + -48 = 0 0 + x = -45.254833996 + -48 x = -45.254833996 + -48 Combine like terms: -45.254833996 + -48 = -93.254833996 x = -93.254833996 Simplifying x = -93.254833996Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.745166004, -93.254833996}
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