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Simplifying 6 = 0.0002x2 + -0.316x + 121.9 Reorder the terms: 6 = 121.9 + -0.316x + 0.0002x2 Solving 6 = 121.9 + -0.316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 6 + -121.9 = -115.9 -115.9 + 0.316x + -0.0002x2 = 121.9 + -0.316x + 0.0002x2 + -121.9 + 0.316x + -0.0002x2 Reorder the terms: -115.9 + 0.316x + -0.0002x2 = 121.9 + -121.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: 121.9 + -121.9 = 0.0 -115.9 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -115.9 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -115.9 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -115.9 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -115.9 + 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'. 579500 + -1580x + x2 = 0 Move the constant term to the right: Add '-579500' to each side of the equation. 579500 + -1580x + -579500 + x2 = 0 + -579500 Reorder the terms: 579500 + -579500 + -1580x + x2 = 0 + -579500 Combine like terms: 579500 + -579500 = 0 0 + -1580x + x2 = 0 + -579500 -1580x + x2 = 0 + -579500 Combine like terms: 0 + -579500 = -579500 -1580x + x2 = -579500 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 = -579500 + 624100 Reorder the terms: 624100 + -1580x + x2 = -579500 + 624100 Combine like terms: -579500 + 624100 = 44600 624100 + -1580x + x2 = 44600 Factor a perfect square on the left side: (x + -790)(x + -790) = 44600 Calculate the square root of the right side: 211.187120819 Break this problem into two subproblems by setting (x + -790) equal to 211.187120819 and -211.187120819.Subproblem 1
x + -790 = 211.187120819 Simplifying x + -790 = 211.187120819 Reorder the terms: -790 + x = 211.187120819 Solving -790 + x = 211.187120819 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 = 211.187120819 + 790 Combine like terms: -790 + 790 = 0 0 + x = 211.187120819 + 790 x = 211.187120819 + 790 Combine like terms: 211.187120819 + 790 = 1001.187120819 x = 1001.187120819 Simplifying x = 1001.187120819Subproblem 2
x + -790 = -211.187120819 Simplifying x + -790 = -211.187120819 Reorder the terms: -790 + x = -211.187120819 Solving -790 + x = -211.187120819 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 = -211.187120819 + 790 Combine like terms: -790 + 790 = 0 0 + x = -211.187120819 + 790 x = -211.187120819 + 790 Combine like terms: -211.187120819 + 790 = 578.812879181 x = 578.812879181 Simplifying x = 578.812879181Solution
The solution to the problem is based on the solutions from the subproblems. x = {1001.187120819, 578.812879181}
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