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Simplifying 0 = -85 + 175x + -16x2 Solving 0 = -85 + 175x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 85 = 85 85 + -175x + 16x2 = -85 + 175x + -16x2 + 85 + -175x + 16x2 Reorder the terms: 85 + -175x + 16x2 = -85 + 85 + 175x + -175x + -16x2 + 16x2 Combine like terms: -85 + 85 = 0 85 + -175x + 16x2 = 0 + 175x + -175x + -16x2 + 16x2 85 + -175x + 16x2 = 175x + -175x + -16x2 + 16x2 Combine like terms: 175x + -175x = 0 85 + -175x + 16x2 = 0 + -16x2 + 16x2 85 + -175x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 85 + -175x + 16x2 = 0 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 = 24.59472656 29.90722656 + -10.9375x + x2 = 24.59472656 Factor a perfect square on the left side: (x + -5.46875)(x + -5.46875) = 24.59472656 Calculate the square root of the right side: 4.959307065 Break this problem into two subproblems by setting (x + -5.46875) equal to 4.959307065 and -4.959307065.Subproblem 1
x + -5.46875 = 4.959307065 Simplifying x + -5.46875 = 4.959307065 Reorder the terms: -5.46875 + x = 4.959307065 Solving -5.46875 + x = 4.959307065 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 = 4.959307065 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + x = 4.959307065 + 5.46875 x = 4.959307065 + 5.46875 Combine like terms: 4.959307065 + 5.46875 = 10.428057065 x = 10.428057065 Simplifying x = 10.428057065Subproblem 2
x + -5.46875 = -4.959307065 Simplifying x + -5.46875 = -4.959307065 Reorder the terms: -5.46875 + x = -4.959307065 Solving -5.46875 + x = -4.959307065 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 = -4.959307065 + 5.46875 Combine like terms: -5.46875 + 5.46875 = 0.00000 0.00000 + x = -4.959307065 + 5.46875 x = -4.959307065 + 5.46875 Combine like terms: -4.959307065 + 5.46875 = 0.509442935 x = 0.509442935 Simplifying x = 0.509442935Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.428057065, 0.509442935}
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