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Simplifying -16x2 + 175x + 85 = 0 Reorder the terms: 85 + 175x + -16x2 = 0 Solving 85 + 175x + -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'. -5.3125 + -10.9375x + x2 = 0 Move the constant term to the right: Add '5.3125' to each side of the equation. -5.3125 + -10.9375x + 5.3125 + x2 = 0 + 5.3125 Reorder the terms: -5.3125 + 5.3125 + -10.9375x + x2 = 0 + 5.3125 Combine like terms: -5.3125 + 5.3125 = 0.0000 0.0000 + -10.9375x + x2 = 0 + 5.3125 -10.9375x + x2 = 0 + 5.3125 Combine like terms: 0 + 5.3125 = 5.3125 -10.9375x + x2 = 5.3125 The x term is -10.9375x. Take half its coefficient (-5.46875). Square it (29.90722656) and add it to both sides. Add '29.90722656' to each side of the equation. -10.9375x + 29.90722656 + x2 = 5.3125 + 29.90722656 Reorder the terms: 29.90722656 + -10.9375x + x2 = 5.3125 + 29.90722656 Combine like terms: 5.3125 + 29.90722656 = 35.21972656 29.90722656 + -10.9375x + x2 = 35.21972656 Factor a perfect square on the left side: (x + -5.46875)(x + -5.46875) = 35.21972656 Calculate the square root of the right side: 5.934621012 Break this problem into two subproblems by setting (x + -5.46875) equal to 5.934621012 and -5.934621012.Subproblem 1
x + -5.46875 = 5.934621012 Simplifying x + -5.46875 = 5.934621012 Reorder the terms: -5.46875 + x = 5.934621012 Solving -5.46875 + x = 5.934621012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + x = 5.934621012 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + x = 5.934621012 + 5.46875 x = 5.934621012 + 5.46875 Combine like terms: 5.934621012 + 5.46875 = 11.403371012 x = 11.403371012 Simplifying x = 11.403371012Subproblem 2
x + -5.46875 = -5.934621012 Simplifying x + -5.46875 = -5.934621012 Reorder the terms: -5.46875 + x = -5.934621012 Solving -5.46875 + x = -5.934621012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.46875' to each side of the equation. -5.46875 + 5.46875 + x = -5.934621012 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + x = -5.934621012 + 5.46875 x = -5.934621012 + 5.46875 Combine like terms: -5.934621012 + 5.46875 = -0.465871012 x = -0.465871012 Simplifying x = -0.465871012Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.403371012, -0.465871012}
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