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Simplifying x2 + -8x + -320 = 0 Reorder the terms: -320 + -8x + x2 = 0 Solving -320 + -8x + 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 + -8x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + -8x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + -8x + x2 = 0 + 320 -8x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 -8x + x2 = 320 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 320 + 16 Reorder the terms: 16 + -8x + x2 = 320 + 16 Combine like terms: 320 + 16 = 336 16 + -8x + x2 = 336 Factor a perfect square on the left side: (x + -4)(x + -4) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + -4) equal to 18.33030278 and -18.33030278.Subproblem 1
x + -4 = 18.33030278 Simplifying x + -4 = 18.33030278 Reorder the terms: -4 + x = 18.33030278 Solving -4 + x = 18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 18.33030278 + 4 Combine like terms: -4 + 4 = 0 0 + x = 18.33030278 + 4 x = 18.33030278 + 4 Combine like terms: 18.33030278 + 4 = 22.33030278 x = 22.33030278 Simplifying x = 22.33030278Subproblem 2
x + -4 = -18.33030278 Simplifying x + -4 = -18.33030278 Reorder the terms: -4 + x = -18.33030278 Solving -4 + x = -18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -18.33030278 + 4 Combine like terms: -4 + 4 = 0 0 + x = -18.33030278 + 4 x = -18.33030278 + 4 Combine like terms: -18.33030278 + 4 = -14.33030278 x = -14.33030278 Simplifying x = -14.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.33030278, -14.33030278}
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