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Simplifying -16x2 + 272x + -85 = 0 Reorder the terms: -85 + 272x + -16x2 = 0 Solving -85 + 272x + -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'. 5.3125 + -17x + x2 = 0 Move the constant term to the right: Add '-5.3125' to each side of the equation. 5.3125 + -17x + -5.3125 + x2 = 0 + -5.3125 Reorder the terms: 5.3125 + -5.3125 + -17x + x2 = 0 + -5.3125 Combine like terms: 5.3125 + -5.3125 = 0.0000 0.0000 + -17x + x2 = 0 + -5.3125 -17x + x2 = 0 + -5.3125 Combine like terms: 0 + -5.3125 = -5.3125 -17x + x2 = -5.3125 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -5.3125 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -5.3125 + 72.25 Combine like terms: -5.3125 + 72.25 = 66.9375 72.25 + -17x + x2 = 66.9375 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 66.9375 Calculate the square root of the right side: 8.181534086 Break this problem into two subproblems by setting (x + -8.5) equal to 8.181534086 and -8.181534086.Subproblem 1
x + -8.5 = 8.181534086 Simplifying x + -8.5 = 8.181534086 Reorder the terms: -8.5 + x = 8.181534086 Solving -8.5 + x = 8.181534086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.181534086 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.181534086 + 8.5 x = 8.181534086 + 8.5 Combine like terms: 8.181534086 + 8.5 = 16.681534086 x = 16.681534086 Simplifying x = 16.681534086Subproblem 2
x + -8.5 = -8.181534086 Simplifying x + -8.5 = -8.181534086 Reorder the terms: -8.5 + x = -8.181534086 Solving -8.5 + x = -8.181534086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.181534086 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.181534086 + 8.5 x = -8.181534086 + 8.5 Combine like terms: -8.181534086 + 8.5 = 0.318465914 x = 0.318465914 Simplifying x = 0.318465914Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.681534086, 0.318465914}
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