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Simplifying x = 0.0002x2 + -0.316x + 127.9 Reorder the terms: x = 127.9 + -0.316x + 0.0002x2 Solving x = 127.9 + -0.316x + 0.0002x2 Solving for variable 'x'. Reorder the terms: -127.9 + x + 0.316x + -0.0002x2 = 127.9 + -0.316x + 0.0002x2 + -127.9 + 0.316x + -0.0002x2 Combine like terms: x + 0.316x = 1.316x -127.9 + 1.316x + -0.0002x2 = 127.9 + -0.316x + 0.0002x2 + -127.9 + 0.316x + -0.0002x2 Reorder the terms: -127.9 + 1.316x + -0.0002x2 = 127.9 + -127.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: 127.9 + -127.9 = 0.0 -127.9 + 1.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -127.9 + 1.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -127.9 + 1.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -127.9 + 1.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -127.9 + 1.316x + -0.0002x2 = 0.0000 Begin completing the square. Divide all terms by -0.0002 the coefficient of the squared term: Divide each side by '-0.0002'. 639500 + -6580x + x2 = 0 Move the constant term to the right: Add '-639500' to each side of the equation. 639500 + -6580x + -639500 + x2 = 0 + -639500 Reorder the terms: 639500 + -639500 + -6580x + x2 = 0 + -639500 Combine like terms: 639500 + -639500 = 0 0 + -6580x + x2 = 0 + -639500 -6580x + x2 = 0 + -639500 Combine like terms: 0 + -639500 = -639500 -6580x + x2 = -639500 The x term is -6580x. Take half its coefficient (-3290). Square it (10824100) and add it to both sides. Add '10824100' to each side of the equation. -6580x + 10824100 + x2 = -639500 + 10824100 Reorder the terms: 10824100 + -6580x + x2 = -639500 + 10824100 Combine like terms: -639500 + 10824100 = 10184600 10824100 + -6580x + x2 = 10184600 Factor a perfect square on the left side: (x + -3290)(x + -3290) = 10184600 Calculate the square root of the right side: 3191.332010305 Break this problem into two subproblems by setting (x + -3290) equal to 3191.332010305 and -3191.332010305.Subproblem 1
x + -3290 = 3191.332010305 Simplifying x + -3290 = 3191.332010305 Reorder the terms: -3290 + x = 3191.332010305 Solving -3290 + x = 3191.332010305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3290' to each side of the equation. -3290 + 3290 + x = 3191.332010305 + 3290 Combine like terms: -3290 + 3290 = 0 0 + x = 3191.332010305 + 3290 x = 3191.332010305 + 3290 Combine like terms: 3191.332010305 + 3290 = 6481.332010305 x = 6481.332010305 Simplifying x = 6481.332010305Subproblem 2
x + -3290 = -3191.332010305 Simplifying x + -3290 = -3191.332010305 Reorder the terms: -3290 + x = -3191.332010305 Solving -3290 + x = -3191.332010305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3290' to each side of the equation. -3290 + 3290 + x = -3191.332010305 + 3290 Combine like terms: -3290 + 3290 = 0 0 + x = -3191.332010305 + 3290 x = -3191.332010305 + 3290 Combine like terms: -3191.332010305 + 3290 = 98.667989695 x = 98.667989695 Simplifying x = 98.667989695Solution
The solution to the problem is based on the solutions from the subproblems. x = {6481.332010305, 98.667989695}
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