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Simplifying 9 = 0.0002x2 + -0.316x + 118.9 Reorder the terms: 9 = 118.9 + -0.316x + 0.0002x2 Solving 9 = 118.9 + -0.316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 9 + -118.9 = -109.9 -109.9 + 0.316x + -0.0002x2 = 118.9 + -0.316x + 0.0002x2 + -118.9 + 0.316x + -0.0002x2 Reorder the terms: -109.9 + 0.316x + -0.0002x2 = 118.9 + -118.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: 118.9 + -118.9 = 0.0 -109.9 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2 -109.9 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2 Combine like terms: -0.316x + 0.316x = 0.000 -109.9 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 -109.9 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -109.9 + 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'. 549500 + -1580x + x2 = 0 Move the constant term to the right: Add '-549500' to each side of the equation. 549500 + -1580x + -549500 + x2 = 0 + -549500 Reorder the terms: 549500 + -549500 + -1580x + x2 = 0 + -549500 Combine like terms: 549500 + -549500 = 0 0 + -1580x + x2 = 0 + -549500 -1580x + x2 = 0 + -549500 Combine like terms: 0 + -549500 = -549500 -1580x + x2 = -549500 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 = -549500 + 624100 Reorder the terms: 624100 + -1580x + x2 = -549500 + 624100 Combine like terms: -549500 + 624100 = 74600 624100 + -1580x + x2 = 74600 Factor a perfect square on the left side: (x + -790)(x + -790) = 74600 Calculate the square root of the right side: 273.130005675 Break this problem into two subproblems by setting (x + -790) equal to 273.130005675 and -273.130005675.Subproblem 1
x + -790 = 273.130005675 Simplifying x + -790 = 273.130005675 Reorder the terms: -790 + x = 273.130005675 Solving -790 + x = 273.130005675 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 = 273.130005675 + 790 Combine like terms: -790 + 790 = 0 0 + x = 273.130005675 + 790 x = 273.130005675 + 790 Combine like terms: 273.130005675 + 790 = 1063.130005675 x = 1063.130005675 Simplifying x = 1063.130005675Subproblem 2
x + -790 = -273.130005675 Simplifying x + -790 = -273.130005675 Reorder the terms: -790 + x = -273.130005675 Solving -790 + x = -273.130005675 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 = -273.130005675 + 790 Combine like terms: -790 + 790 = 0 0 + x = -273.130005675 + 790 x = -273.130005675 + 790 Combine like terms: -273.130005675 + 790 = 516.869994325 x = 516.869994325 Simplifying x = 516.869994325Solution
The solution to the problem is based on the solutions from the subproblems. x = {1063.130005675, 516.869994325}
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