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Simplifying x2 + -64x + -320 = 0 Reorder the terms: -320 + -64x + x2 = 0 Solving -320 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + -64x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + -64x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + -64x + x2 = 0 + 320 -64x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 -64x + x2 = 320 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 = 320 + 1024 Reorder the terms: 1024 + -64x + x2 = 320 + 1024 Combine like terms: 320 + 1024 = 1344 1024 + -64x + x2 = 1344 Factor a perfect square on the left side: (x + -32)(x + -32) = 1344 Calculate the square root of the right side: 36.66060556 Break this problem into two subproblems by setting (x + -32) equal to 36.66060556 and -36.66060556.Subproblem 1
x + -32 = 36.66060556 Simplifying x + -32 = 36.66060556 Reorder the terms: -32 + x = 36.66060556 Solving -32 + x = 36.66060556 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 = 36.66060556 + 32 Combine like terms: -32 + 32 = 0 0 + x = 36.66060556 + 32 x = 36.66060556 + 32 Combine like terms: 36.66060556 + 32 = 68.66060556 x = 68.66060556 Simplifying x = 68.66060556Subproblem 2
x + -32 = -36.66060556 Simplifying x + -32 = -36.66060556 Reorder the terms: -32 + x = -36.66060556 Solving -32 + x = -36.66060556 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 = -36.66060556 + 32 Combine like terms: -32 + 32 = 0 0 + x = -36.66060556 + 32 x = -36.66060556 + 32 Combine like terms: -36.66060556 + 32 = -4.66060556 x = -4.66060556 Simplifying x = -4.66060556Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.66060556, -4.66060556}
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