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Simplifying x2 + -32x + -80 = 0 Reorder the terms: -80 + -32x + x2 = 0 Solving -80 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -32x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -32x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -32x + x2 = 0 + 80 -32x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -32x + x2 = 80 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 80 + 256 Reorder the terms: 256 + -32x + x2 = 80 + 256 Combine like terms: 80 + 256 = 336 256 + -32x + x2 = 336 Factor a perfect square on the left side: (x + -16)(x + -16) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + -16) equal to 18.33030278 and -18.33030278.Subproblem 1
x + -16 = 18.33030278 Simplifying x + -16 = 18.33030278 Reorder the terms: -16 + x = 18.33030278 Solving -16 + x = 18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 18.33030278 + 16 Combine like terms: -16 + 16 = 0 0 + x = 18.33030278 + 16 x = 18.33030278 + 16 Combine like terms: 18.33030278 + 16 = 34.33030278 x = 34.33030278 Simplifying x = 34.33030278Subproblem 2
x + -16 = -18.33030278 Simplifying x + -16 = -18.33030278 Reorder the terms: -16 + x = -18.33030278 Solving -16 + x = -18.33030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -18.33030278 + 16 Combine like terms: -16 + 16 = 0 0 + x = -18.33030278 + 16 x = -18.33030278 + 16 Combine like terms: -18.33030278 + 16 = -2.33030278 x = -2.33030278 Simplifying x = -2.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.33030278, -2.33030278}
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