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Simplifying x2 + -64x + -2304 = 0 Reorder the terms: -2304 + -64x + x2 = 0 Solving -2304 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2304' to each side of the equation. -2304 + -64x + 2304 + x2 = 0 + 2304 Reorder the terms: -2304 + 2304 + -64x + x2 = 0 + 2304 Combine like terms: -2304 + 2304 = 0 0 + -64x + x2 = 0 + 2304 -64x + x2 = 0 + 2304 Combine like terms: 0 + 2304 = 2304 -64x + x2 = 2304 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = 2304 + 1024 Reorder the terms: 1024 + -64x + x2 = 2304 + 1024 Combine like terms: 2304 + 1024 = 3328 1024 + -64x + x2 = 3328 Factor a perfect square on the left side: (x + -32)(x + -32) = 3328 Calculate the square root of the right side: 57.688820407 Break this problem into two subproblems by setting (x + -32) equal to 57.688820407 and -57.688820407.Subproblem 1
x + -32 = 57.688820407 Simplifying x + -32 = 57.688820407 Reorder the terms: -32 + x = 57.688820407 Solving -32 + x = 57.688820407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 57.688820407 + 32 Combine like terms: -32 + 32 = 0 0 + x = 57.688820407 + 32 x = 57.688820407 + 32 Combine like terms: 57.688820407 + 32 = 89.688820407 x = 89.688820407 Simplifying x = 89.688820407Subproblem 2
x + -32 = -57.688820407 Simplifying x + -32 = -57.688820407 Reorder the terms: -32 + x = -57.688820407 Solving -32 + x = -57.688820407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -57.688820407 + 32 Combine like terms: -32 + 32 = 0 0 + x = -57.688820407 + 32 x = -57.688820407 + 32 Combine like terms: -57.688820407 + 32 = -25.688820407 x = -25.688820407 Simplifying x = -25.688820407Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.688820407, -25.688820407}
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