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Simplifying 0 = -16x2 + 3.3x + 85 Reorder the terms: 0 = 85 + 3.3x + -16x2 Solving 0 = 85 + 3.3x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -85 = -85 -85 + -3.3x + 16x2 = 85 + 3.3x + -16x2 + -85 + -3.3x + 16x2 Reorder the terms: -85 + -3.3x + 16x2 = 85 + -85 + 3.3x + -3.3x + -16x2 + 16x2 Combine like terms: 85 + -85 = 0 -85 + -3.3x + 16x2 = 0 + 3.3x + -3.3x + -16x2 + 16x2 -85 + -3.3x + 16x2 = 3.3x + -3.3x + -16x2 + 16x2 Combine like terms: 3.3x + -3.3x = 0.0 -85 + -3.3x + 16x2 = 0.0 + -16x2 + 16x2 -85 + -3.3x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -85 + -3.3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.3125 + -0.20625x + x2 = 0 Move the constant term to the right: Add '5.3125' to each side of the equation. -5.3125 + -0.20625x + 5.3125 + x2 = 0 + 5.3125 Reorder the terms: -5.3125 + 5.3125 + -0.20625x + x2 = 0 + 5.3125 Combine like terms: -5.3125 + 5.3125 = 0.0000 0.0000 + -0.20625x + x2 = 0 + 5.3125 -0.20625x + x2 = 0 + 5.3125 Combine like terms: 0 + 5.3125 = 5.3125 -0.20625x + x2 = 5.3125 The x term is -0.20625x. Take half its coefficient (-0.103125). Square it (0.01063476563) and add it to both sides. Add '0.01063476563' to each side of the equation. -0.20625x + 0.01063476563 + x2 = 5.3125 + 0.01063476563 Reorder the terms: 0.01063476563 + -0.20625x + x2 = 5.3125 + 0.01063476563 Combine like terms: 5.3125 + 0.01063476563 = 5.32313476563 0.01063476563 + -0.20625x + x2 = 5.32313476563 Factor a perfect square on the left side: (x + -0.103125)(x + -0.103125) = 5.32313476563 Calculate the square root of the right side: 2.307191965 Break this problem into two subproblems by setting (x + -0.103125) equal to 2.307191965 and -2.307191965.Subproblem 1
x + -0.103125 = 2.307191965 Simplifying x + -0.103125 = 2.307191965 Reorder the terms: -0.103125 + x = 2.307191965 Solving -0.103125 + x = 2.307191965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.103125' to each side of the equation. -0.103125 + 0.103125 + x = 2.307191965 + 0.103125 Combine like terms: -0.103125 + 0.103125 = 0.000000 0.000000 + x = 2.307191965 + 0.103125 x = 2.307191965 + 0.103125 Combine like terms: 2.307191965 + 0.103125 = 2.410316965 x = 2.410316965 Simplifying x = 2.410316965Subproblem 2
x + -0.103125 = -2.307191965 Simplifying x + -0.103125 = -2.307191965 Reorder the terms: -0.103125 + x = -2.307191965 Solving -0.103125 + x = -2.307191965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.103125' to each side of the equation. -0.103125 + 0.103125 + x = -2.307191965 + 0.103125 Combine like terms: -0.103125 + 0.103125 = 0.000000 0.000000 + x = -2.307191965 + 0.103125 x = -2.307191965 + 0.103125 Combine like terms: -2.307191965 + 0.103125 = -2.204066965 x = -2.204066965 Simplifying x = -2.204066965Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.410316965, -2.204066965}
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