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Simplifying 60 = -16x2 + 85x Reorder the terms: 60 = 85x + -16x2 Solving 60 = 85x + -16x2 Solving for variable 'x'. Reorder the terms: 60 + -85x + 16x2 = 85x + -85x + -16x2 + 16x2 Combine like terms: 85x + -85x = 0 60 + -85x + 16x2 = 0 + -16x2 + 16x2 60 + -85x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 60 + -85x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.75 + -5.3125x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -5.3125x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -5.3125x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -5.3125x + x2 = 0 + -3.75 -5.3125x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -5.3125x + x2 = -3.75 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 = -3.75 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125x + x2 = -3.75 + 7.055664063 Combine like terms: -3.75 + 7.055664063 = 3.305664063 7.055664063 + -5.3125x + x2 = 3.305664063 Factor a perfect square on the left side: (x + -2.65625)(x + -2.65625) = 3.305664063 Calculate the square root of the right side: 1.818148526 Break this problem into two subproblems by setting (x + -2.65625) equal to 1.818148526 and -1.818148526.Subproblem 1
x + -2.65625 = 1.818148526 Simplifying x + -2.65625 = 1.818148526 Reorder the terms: -2.65625 + x = 1.818148526 Solving -2.65625 + x = 1.818148526 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 = 1.818148526 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = 1.818148526 + 2.65625 x = 1.818148526 + 2.65625 Combine like terms: 1.818148526 + 2.65625 = 4.474398526 x = 4.474398526 Simplifying x = 4.474398526Subproblem 2
x + -2.65625 = -1.818148526 Simplifying x + -2.65625 = -1.818148526 Reorder the terms: -2.65625 + x = -1.818148526 Solving -2.65625 + x = -1.818148526 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 = -1.818148526 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = -1.818148526 + 2.65625 x = -1.818148526 + 2.65625 Combine like terms: -1.818148526 + 2.65625 = 0.838101474 x = 0.838101474 Simplifying x = 0.838101474Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.474398526, 0.838101474}
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