550=.0002x^2-.316x+127.9

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Solution for 550=.0002x^2-.316x+127.9 equation:


Simplifying
550 = 0.0002x2 + -0.316x + 127.9

Reorder the terms:
550 = 127.9 + -0.316x + 0.0002x2

Solving
550 = 127.9 + -0.316x + 0.0002x2

Solving for variable 'x'.

Combine like terms: 550 + -127.9 = 422.1
422.1 + 0.316x + -0.0002x2 = 127.9 + -0.316x + 0.0002x2 + -127.9 + 0.316x + -0.0002x2

Reorder the terms:
422.1 + 0.316x + -0.0002x2 = 127.9 + -127.9 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2

Combine like terms: 127.9 + -127.9 = 0.0
422.1 + 0.316x + -0.0002x2 = 0.0 + -0.316x + 0.316x + 0.0002x2 + -0.0002x2
422.1 + 0.316x + -0.0002x2 = -0.316x + 0.316x + 0.0002x2 + -0.0002x2

Combine like terms: -0.316x + 0.316x = 0.000
422.1 + 0.316x + -0.0002x2 = 0.000 + 0.0002x2 + -0.0002x2
422.1 + 0.316x + -0.0002x2 = 0.0002x2 + -0.0002x2

Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000
422.1 + 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'.
-2110500 + -1580x + x2 = 0

Move the constant term to the right:

Add '2110500' to each side of the equation.
-2110500 + -1580x + 2110500 + x2 = 0 + 2110500

Reorder the terms:
-2110500 + 2110500 + -1580x + x2 = 0 + 2110500

Combine like terms: -2110500 + 2110500 = 0
0 + -1580x + x2 = 0 + 2110500
-1580x + x2 = 0 + 2110500

Combine like terms: 0 + 2110500 = 2110500
-1580x + x2 = 2110500

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 = 2110500 + 624100

Reorder the terms:
624100 + -1580x + x2 = 2110500 + 624100

Combine like terms: 2110500 + 624100 = 2734600
624100 + -1580x + x2 = 2734600

Factor a perfect square on the left side:
(x + -790)(x + -790) = 2734600

Calculate the square root of the right side: 1653.662601621

Break this problem into two subproblems by setting 
(x + -790) equal to 1653.662601621 and -1653.662601621.

Subproblem 1

x + -790 = 1653.662601621 Simplifying x + -790 = 1653.662601621 Reorder the terms: -790 + x = 1653.662601621 Solving -790 + x = 1653.662601621 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 = 1653.662601621 + 790 Combine like terms: -790 + 790 = 0 0 + x = 1653.662601621 + 790 x = 1653.662601621 + 790 Combine like terms: 1653.662601621 + 790 = 2443.662601621 x = 2443.662601621 Simplifying x = 2443.662601621

Subproblem 2

x + -790 = -1653.662601621 Simplifying x + -790 = -1653.662601621 Reorder the terms: -790 + x = -1653.662601621 Solving -790 + x = -1653.662601621 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 = -1653.662601621 + 790 Combine like terms: -790 + 790 = 0 0 + x = -1653.662601621 + 790 x = -1653.662601621 + 790 Combine like terms: -1653.662601621 + 790 = -863.662601621 x = -863.662601621 Simplifying x = -863.662601621

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2443.662601621, -863.662601621}

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