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Simplifying 85x + -16x2 = 30 Solving 85x + -16x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 85x + -16x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 85x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.875 + -5.3125x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -5.3125x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -5.3125x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -5.3125x + x2 = 0 + -1.875 -5.3125x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -5.3125x + x2 = -1.875 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 = -1.875 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125x + x2 = -1.875 + 7.055664063 Combine like terms: -1.875 + 7.055664063 = 5.180664063 7.055664063 + -5.3125x + x2 = 5.180664063 Factor a perfect square on the left side: (x + -2.65625)(x + -2.65625) = 5.180664063 Calculate the square root of the right side: 2.276107217 Break this problem into two subproblems by setting (x + -2.65625) equal to 2.276107217 and -2.276107217.Subproblem 1
x + -2.65625 = 2.276107217 Simplifying x + -2.65625 = 2.276107217 Reorder the terms: -2.65625 + x = 2.276107217 Solving -2.65625 + x = 2.276107217 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 = 2.276107217 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = 2.276107217 + 2.65625 x = 2.276107217 + 2.65625 Combine like terms: 2.276107217 + 2.65625 = 4.932357217 x = 4.932357217 Simplifying x = 4.932357217Subproblem 2
x + -2.65625 = -2.276107217 Simplifying x + -2.65625 = -2.276107217 Reorder the terms: -2.65625 + x = -2.276107217 Solving -2.65625 + x = -2.276107217 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 = -2.276107217 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = -2.276107217 + 2.65625 x = -2.276107217 + 2.65625 Combine like terms: -2.276107217 + 2.65625 = 0.380142783 x = 0.380142783 Simplifying x = 0.380142783Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.932357217, 0.380142783}
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