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Simplifying 6 = 0.0002x2 + -0.316x + 127.8 Reorder the terms: 6 = 127.8 + -0.316x + 0.0002x2 Solving 6 = 127.8 + -0.316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 6 + -127.8 = -121.8 -121.8 + 0.316x + -0.0002x2 = 127.8 + -0.316x + 0.0002x2 + -127.8 + 0.316x + -0.0002x2 Reorder the terms: -121.8 + 0.316x + -0.0002x2 = 127.8 + -127.8 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: 127.8 + -127.8 = 0.0 -121.8 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -121.8 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -121.8 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -121.8 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -121.8 + 0.316x + -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'. 609000 + -1580x + x2 = 0 Move the constant term to the right: Add '-609000' to each side of the equation. 609000 + -1580x + -609000 + x2 = 0 + -609000 Reorder the terms: 609000 + -609000 + -1580x + x2 = 0 + -609000 Combine like terms: 609000 + -609000 = 0 0 + -1580x + x2 = 0 + -609000 -1580x + x2 = 0 + -609000 Combine like terms: 0 + -609000 = -609000 -1580x + x2 = -609000 The x term is -1580x. Take half its coefficient (-790). Square it (624100) and add it to both sides. Add '624100' to each side of the equation. -1580x + 624100 + x2 = -609000 + 624100 Reorder the terms: 624100 + -1580x + x2 = -609000 + 624100 Combine like terms: -609000 + 624100 = 15100 624100 + -1580x + x2 = 15100 Factor a perfect square on the left side: (x + -790)(x + -790) = 15100 Calculate the square root of the right side: 122.882057274 Break this problem into two subproblems by setting (x + -790) equal to 122.882057274 and -122.882057274.Subproblem 1
x + -790 = 122.882057274 Simplifying x + -790 = 122.882057274 Reorder the terms: -790 + x = 122.882057274 Solving -790 + x = 122.882057274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = 122.882057274 + 790 Combine like terms: -790 + 790 = 0 0 + x = 122.882057274 + 790 x = 122.882057274 + 790 Combine like terms: 122.882057274 + 790 = 912.882057274 x = 912.882057274 Simplifying x = 912.882057274Subproblem 2
x + -790 = -122.882057274 Simplifying x + -790 = -122.882057274 Reorder the terms: -790 + x = -122.882057274 Solving -790 + x = -122.882057274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790' to each side of the equation. -790 + 790 + x = -122.882057274 + 790 Combine like terms: -790 + 790 = 0 0 + x = -122.882057274 + 790 x = -122.882057274 + 790 Combine like terms: -122.882057274 + 790 = 667.117942726 x = 667.117942726 Simplifying x = 667.117942726Solution
The solution to the problem is based on the solutions from the subproblems. x = {912.882057274, 667.117942726}
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