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Simplifying 4 = 0.0002x2 + -0.316x + 127.9x Reorder the terms: 4 = -0.316x + 127.9x + 0.0002x2 Combine like terms: -0.316x + 127.9x = 127.584x 4 = 127.584x + 0.0002x2 Solving 4 = 127.584x + 0.0002x2 Solving for variable 'x'. Reorder the terms: 4 + -127.584x + -0.0002x2 = 127.584x + -127.584x + 0.0002x2 + -0.0002x2 Combine like terms: 127.584x + -127.584x = 0.000 4 + -127.584x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2 4 + -127.584x + -0.0002x2 = 0.0002x2 + -0.0002x2 Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000 4 + -127.584x + -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'. -20000 + 637920x + x2 = 0 Move the constant term to the right: Add '20000' to each side of the equation. -20000 + 637920x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + 637920x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + 637920x + x2 = 0 + 20000 637920x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 637920x + x2 = 20000 The x term is 637920x. Take half its coefficient (318960). Square it (101735481600) and add it to both sides. Add '101735481600' to each side of the equation. 637920x + 101735481600 + x2 = 20000 + 101735481600 Reorder the terms: 101735481600 + 637920x + x2 = 20000 + 101735481600 Combine like terms: 20000 + 101735481600 = 101735501600 101735481600 + 637920x + x2 = 101735501600 Factor a perfect square on the left side: (x + 318960)(x + 318960) = 101735501600 Calculate the square root of the right side: 318960.031351892 Break this problem into two subproblems by setting (x + 318960) equal to 318960.031351892 and -318960.031351892.Subproblem 1
x + 318960 = 318960.031351892 Simplifying x + 318960 = 318960.031351892 Reorder the terms: 318960 + x = 318960.031351892 Solving 318960 + x = 318960.031351892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-318960' to each side of the equation. 318960 + -318960 + x = 318960.031351892 + -318960 Combine like terms: 318960 + -318960 = 0 0 + x = 318960.031351892 + -318960 x = 318960.031351892 + -318960 Combine like terms: 318960.031351892 + -318960 = 0.031351892 x = 0.031351892 Simplifying x = 0.031351892Subproblem 2
x + 318960 = -318960.031351892 Simplifying x + 318960 = -318960.031351892 Reorder the terms: 318960 + x = -318960.031351892 Solving 318960 + x = -318960.031351892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-318960' to each side of the equation. 318960 + -318960 + x = -318960.031351892 + -318960 Combine like terms: 318960 + -318960 = 0 0 + x = -318960.031351892 + -318960 x = -318960.031351892 + -318960 Combine like terms: -318960.031351892 + -318960 = -637920.031351892 x = -637920.031351892 Simplifying x = -637920.031351892Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.031351892, -637920.031351892}
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