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Simplifying -16x2 + 85x + 5 = 0 Reorder the terms: 5 + 85x + -16x2 = 0 Solving 5 + 85x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -5.3125x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -5.3125x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -5.3125x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -5.3125x + x2 = 0 + 0.3125 -5.3125x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -5.3125x + x2 = 0.3125 The x term is -5.3125x. Take half its coefficient (-2.65625). Square it (7.055664063) and add it to both sides. Add '7.055664063' to each side of the equation. -5.3125x + 7.055664063 + x2 = 0.3125 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125x + x2 = 0.3125 + 7.055664063 Combine like terms: 0.3125 + 7.055664063 = 7.368164063 7.055664063 + -5.3125x + x2 = 7.368164063 Factor a perfect square on the left side: (x + -2.65625)(x + -2.65625) = 7.368164063 Calculate the square root of the right side: 2.714436233 Break this problem into two subproblems by setting (x + -2.65625) equal to 2.714436233 and -2.714436233.Subproblem 1
x + -2.65625 = 2.714436233 Simplifying x + -2.65625 = 2.714436233 Reorder the terms: -2.65625 + x = 2.714436233 Solving -2.65625 + x = 2.714436233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.65625' to each side of the equation. -2.65625 + 2.65625 + x = 2.714436233 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = 2.714436233 + 2.65625 x = 2.714436233 + 2.65625 Combine like terms: 2.714436233 + 2.65625 = 5.370686233 x = 5.370686233 Simplifying x = 5.370686233Subproblem 2
x + -2.65625 = -2.714436233 Simplifying x + -2.65625 = -2.714436233 Reorder the terms: -2.65625 + x = -2.714436233 Solving -2.65625 + x = -2.714436233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.65625' to each side of the equation. -2.65625 + 2.65625 + x = -2.714436233 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = -2.714436233 + 2.65625 x = -2.714436233 + 2.65625 Combine like terms: -2.714436233 + 2.65625 = -0.058186233 x = -0.058186233 Simplifying x = -0.058186233Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.370686233, -0.058186233}
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