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Simplifying -16x2 + 85x + 3 = 0 Reorder the terms: 3 + 85x + -16x2 = 0 Solving 3 + 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'. -0.1875 + -5.3125x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -5.3125x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -5.3125x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -5.3125x + x2 = 0 + 0.1875 -5.3125x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -5.3125x + x2 = 0.1875 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 = 0.1875 + 7.055664063 Reorder the terms: 7.055664063 + -5.3125x + x2 = 0.1875 + 7.055664063 Combine like terms: 0.1875 + 7.055664063 = 7.243164063 7.055664063 + -5.3125x + x2 = 7.243164063 Factor a perfect square on the left side: (x + -2.65625)(x + -2.65625) = 7.243164063 Calculate the square root of the right side: 2.691312703 Break this problem into two subproblems by setting (x + -2.65625) equal to 2.691312703 and -2.691312703.Subproblem 1
x + -2.65625 = 2.691312703 Simplifying x + -2.65625 = 2.691312703 Reorder the terms: -2.65625 + x = 2.691312703 Solving -2.65625 + x = 2.691312703 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 = 2.691312703 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = 2.691312703 + 2.65625 x = 2.691312703 + 2.65625 Combine like terms: 2.691312703 + 2.65625 = 5.347562703 x = 5.347562703 Simplifying x = 5.347562703Subproblem 2
x + -2.65625 = -2.691312703 Simplifying x + -2.65625 = -2.691312703 Reorder the terms: -2.65625 + x = -2.691312703 Solving -2.65625 + x = -2.691312703 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 = -2.691312703 + 2.65625 Combine like terms: -2.65625 + 2.65625 = 0.00000 0.00000 + x = -2.691312703 + 2.65625 x = -2.691312703 + 2.65625 Combine like terms: -2.691312703 + 2.65625 = -0.035062703 x = -0.035062703 Simplifying x = -0.035062703Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.347562703, -0.035062703}
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