.00002x^2-.316x+1229=0

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Solution for .00002x^2-.316x+1229=0 equation:


Simplifying
0.00002x2 + -0.316x + 1229 = 0

Reorder the terms:
1229 + -0.316x + 0.00002x2 = 0

Solving
1229 + -0.316x + 0.00002x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.00002 the coefficient of the squared term: 

Divide each side by '0.00002'.
61450000 + -15800x + x2 = 0

Move the constant term to the right:

Add '-61450000' to each side of the equation.
61450000 + -15800x + -61450000 + x2 = 0 + -61450000

Reorder the terms:
61450000 + -61450000 + -15800x + x2 = 0 + -61450000

Combine like terms: 61450000 + -61450000 = 0
0 + -15800x + x2 = 0 + -61450000
-15800x + x2 = 0 + -61450000

Combine like terms: 0 + -61450000 = -61450000
-15800x + x2 = -61450000

The x term is -15800x.  Take half its coefficient (-7900).
Square it (62410000) and add it to both sides.

Add '62410000' to each side of the equation.
-15800x + 62410000 + x2 = -61450000 + 62410000

Reorder the terms:
62410000 + -15800x + x2 = -61450000 + 62410000

Combine like terms: -61450000 + 62410000 = 960000
62410000 + -15800x + x2 = 960000

Factor a perfect square on the left side:
(x + -7900)(x + -7900) = 960000

Calculate the square root of the right side: 979.795897113

Break this problem into two subproblems by setting 
(x + -7900) equal to 979.795897113 and -979.795897113.

Subproblem 1

x + -7900 = 979.795897113 Simplifying x + -7900 = 979.795897113 Reorder the terms: -7900 + x = 979.795897113 Solving -7900 + x = 979.795897113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7900' to each side of the equation. -7900 + 7900 + x = 979.795897113 + 7900 Combine like terms: -7900 + 7900 = 0 0 + x = 979.795897113 + 7900 x = 979.795897113 + 7900 Combine like terms: 979.795897113 + 7900 = 8879.795897113 x = 8879.795897113 Simplifying x = 8879.795897113

Subproblem 2

x + -7900 = -979.795897113 Simplifying x + -7900 = -979.795897113 Reorder the terms: -7900 + x = -979.795897113 Solving -7900 + x = -979.795897113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7900' to each side of the equation. -7900 + 7900 + x = -979.795897113 + 7900 Combine like terms: -7900 + 7900 = 0 0 + x = -979.795897113 + 7900 x = -979.795897113 + 7900 Combine like terms: -979.795897113 + 7900 = 6920.204102887 x = 6920.204102887 Simplifying x = 6920.204102887

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8879.795897113, 6920.204102887}

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