7=.0002x^2-316x+127.9

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Solution for 7=.0002x^2-316x+127.9 equation:


Simplifying
7 = 0.0002x2 + -316x + 127.9

Reorder the terms:
7 = 127.9 + -316x + 0.0002x2

Solving
7 = 127.9 + -316x + 0.0002x2

Solving for variable 'x'.

Combine like terms: 7 + -127.9 = -120.9
-120.9 + 316x + -0.0002x2 = 127.9 + -316x + 0.0002x2 + -127.9 + 316x + -0.0002x2

Reorder the terms:
-120.9 + 316x + -0.0002x2 = 127.9 + -127.9 + -316x + 316x + 0.0002x2 + -0.0002x2

Combine like terms: 127.9 + -127.9 = 0.0
-120.9 + 316x + -0.0002x2 = 0.0 + -316x + 316x + 0.0002x2 + -0.0002x2
-120.9 + 316x + -0.0002x2 = -316x + 316x + 0.0002x2 + -0.0002x2

Combine like terms: -316x + 316x = 0
-120.9 + 316x + -0.0002x2 = 0 + 0.0002x2 + -0.0002x2
-120.9 + 316x + -0.0002x2 = 0.0002x2 + -0.0002x2

Combine like terms: 0.0002x2 + -0.0002x2 = 0.0000
-120.9 + 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'.
604500 + -1580000x + x2 = 0

Move the constant term to the right:

Add '-604500' to each side of the equation.
604500 + -1580000x + -604500 + x2 = 0 + -604500

Reorder the terms:
604500 + -604500 + -1580000x + x2 = 0 + -604500

Combine like terms: 604500 + -604500 = 0
0 + -1580000x + x2 = 0 + -604500
-1580000x + x2 = 0 + -604500

Combine like terms: 0 + -604500 = -604500
-1580000x + x2 = -604500

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 = -604500 + 624100000000

Reorder the terms:
624100000000 + -1580000x + x2 = -604500 + 624100000000

Combine like terms: -604500 + 624100000000 = 624099395500
624100000000 + -1580000x + x2 = 624099395500

Factor a perfect square on the left side:
(x + -790000)(x + -790000) = 624099395500

Calculate the square root of the right side: 789999.617404971

Break this problem into two subproblems by setting 
(x + -790000) equal to 789999.617404971 and -789999.617404971.

Subproblem 1

x + -790000 = 789999.617404971 Simplifying x + -790000 = 789999.617404971 Reorder the terms: -790000 + x = 789999.617404971 Solving -790000 + x = 789999.617404971 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 = 789999.617404971 + 790000 Combine like terms: -790000 + 790000 = 0 0 + x = 789999.617404971 + 790000 x = 789999.617404971 + 790000 Combine like terms: 789999.617404971 + 790000 = 1579999.617404971 x = 1579999.617404971 Simplifying x = 1579999.617404971

Subproblem 2

x + -790000 = -789999.617404971 Simplifying x + -790000 = -789999.617404971 Reorder the terms: -790000 + x = -789999.617404971 Solving -790000 + x = -789999.617404971 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 = -789999.617404971 + 790000 Combine like terms: -790000 + 790000 = 0 0 + x = -789999.617404971 + 790000 x = -789999.617404971 + 790000 Combine like terms: -789999.617404971 + 790000 = 0.382595029 x = 0.382595029 Simplifying x = 0.382595029

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1579999.617404971, 0.382595029}

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