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Simplifying 8 = 0.0002x2 + -0.316x + 127.8 Reorder the terms: 8 = 127.8 + -0.316x + 0.0002x2 Solving 8 = 127.8 + -0.316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 8 + -127.8 = -119.8 -119.8 + 0.316x + -0.0002x2 = 127.8 + -0.316x + 0.0002x2 + -127.8 + 0.316x + -0.0002x2 Reorder the terms: -119.8 + 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 -119.8 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -119.8 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -119.8 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -119.8 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -119.8 + 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'. 599000 + -1580x + x2 = 0 Move the constant term to the right: Add '-599000' to each side of the equation. 599000 + -1580x + -599000 + x2 = 0 + -599000 Reorder the terms: 599000 + -599000 + -1580x + x2 = 0 + -599000 Combine like terms: 599000 + -599000 = 0 0 + -1580x + x2 = 0 + -599000 -1580x + x2 = 0 + -599000 Combine like terms: 0 + -599000 = -599000 -1580x + x2 = -599000 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 = -599000 + 624100 Reorder the terms: 624100 + -1580x + x2 = -599000 + 624100 Combine like terms: -599000 + 624100 = 25100 624100 + -1580x + x2 = 25100 Factor a perfect square on the left side: (x + -790)(x + -790) = 25100 Calculate the square root of the right side: 158.429795178 Break this problem into two subproblems by setting (x + -790) equal to 158.429795178 and -158.429795178.Subproblem 1
x + -790 = 158.429795178 Simplifying x + -790 = 158.429795178 Reorder the terms: -790 + x = 158.429795178 Solving -790 + x = 158.429795178 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 = 158.429795178 + 790 Combine like terms: -790 + 790 = 0 0 + x = 158.429795178 + 790 x = 158.429795178 + 790 Combine like terms: 158.429795178 + 790 = 948.429795178 x = 948.429795178 Simplifying x = 948.429795178Subproblem 2
x + -790 = -158.429795178 Simplifying x + -790 = -158.429795178 Reorder the terms: -790 + x = -158.429795178 Solving -790 + x = -158.429795178 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 = -158.429795178 + 790 Combine like terms: -790 + 790 = 0 0 + x = -158.429795178 + 790 x = -158.429795178 + 790 Combine like terms: -158.429795178 + 790 = 631.570204822 x = 631.570204822 Simplifying x = 631.570204822Solution
The solution to the problem is based on the solutions from the subproblems. x = {948.429795178, 631.570204822}
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