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Simplifying 9 = 0.0002x2 + -316x + 127.9 Reorder the terms: 9 = 127.9 + -316x + 0.0002x2 Solving 9 = 127.9 + -316x + 0.0002x2 Solving for variable 'x'. Combine like terms: 9 + -127.9 = -118.9 -118.9 + 316x + -0.0002x2 = 127.9 + -316x + 0.0002x2 + -127.9 + 316x + -0.0002x2 Reorder the terms: -118.9 + 316x + -0.0002x2 = 127.9 + -127.9 + -316x + 316x + 0.0002x2 + -0.0002x2 Combine like terms: 127.9 + -127.9 = 0.0 -118.9 + 316x + -0.0002x2 = 0.0 + -316x + 316x + 0.0002x2 + -0.0002x2 -118.9 + 316x + -0.0002x2 = -316x + 316x + 0.0002x2 + -0.0002x2 Combine like terms: -316x + 316x = 0 -118.9 + 316x + -0.0002x2 = 0 + 0.0002x2 + -0.0002x2 -118.9 + 316x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 -118.9 + 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'. 594500 + -1580000x + x2 = 0 Move the constant term to the right: Add '-594500' to each side of the equation. 594500 + -1580000x + -594500 + x2 = 0 + -594500 Reorder the terms: 594500 + -594500 + -1580000x + x2 = 0 + -594500 Combine like terms: 594500 + -594500 = 0 0 + -1580000x + x2 = 0 + -594500 -1580000x + x2 = 0 + -594500 Combine like terms: 0 + -594500 = -594500 -1580000x + x2 = -594500 The x term is -1580000x. Take half its coefficient (-790000). Square it (624100000000) and add it to both sides. Add '624100000000' to each side of the equation. -1580000x + 624100000000 + x2 = -594500 + 624100000000 Reorder the terms: 624100000000 + -1580000x + x2 = -594500 + 624100000000 Combine like terms: -594500 + 624100000000 = 624099405500 624100000000 + -1580000x + x2 = 624099405500 Factor a perfect square on the left side: (x + -790000)(x + -790000) = 624099405500 Calculate the square root of the right side: 789999.623734088 Break this problem into two subproblems by setting (x + -790000) equal to 789999.623734088 and -789999.623734088.Subproblem 1
x + -790000 = 789999.623734088 Simplifying x + -790000 = 789999.623734088 Reorder the terms: -790000 + x = 789999.623734088 Solving -790000 + x = 789999.623734088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790000' to each side of the equation. -790000 + 790000 + x = 789999.623734088 + 790000 Combine like terms: -790000 + 790000 = 0 0 + x = 789999.623734088 + 790000 x = 789999.623734088 + 790000 Combine like terms: 789999.623734088 + 790000 = 1579999.623734088 x = 1579999.623734088 Simplifying x = 1579999.623734088Subproblem 2
x + -790000 = -789999.623734088 Simplifying x + -790000 = -789999.623734088 Reorder the terms: -790000 + x = -789999.623734088 Solving -790000 + x = -789999.623734088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '790000' to each side of the equation. -790000 + 790000 + x = -789999.623734088 + 790000 Combine like terms: -790000 + 790000 = 0 0 + x = -789999.623734088 + 790000 x = -789999.623734088 + 790000 Combine like terms: -789999.623734088 + 790000 = 0.376265912 x = 0.376265912 Simplifying x = 0.376265912Solution
The solution to the problem is based on the solutions from the subproblems. x = {1579999.623734088, 0.376265912}
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