.20x^2-6x-7000=0

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Solution for .20x^2-6x-7000=0 equation: 


Simplifying
0.20x2 + -6x + -7000 = 0

Reorder the terms:
-7000 + -6x + 0.20x2 = 0

Solving
-7000 + -6x + 0.20x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.20'.
-35000 + -30x + x2 = 0

Move the constant term to the right:

Add '35000' to each side of the equation.
-35000 + -30x + 35000 + x2 = 0 + 35000

Reorder the terms:
-35000 + 35000 + -30x + x2 = 0 + 35000

Combine like terms: -35000 + 35000 = 0
0 + -30x + x2 = 0 + 35000
-30x + x2 = 0 + 35000

Combine like terms: 0 + 35000 = 35000
-30x + x2 = 35000

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 35000 + 225

Reorder the terms:
225 + -30x + x2 = 35000 + 225

Combine like terms: 35000 + 225 = 35225
225 + -30x + x2 = 35225

Factor a perfect square on the left side:
(x + -15)(x + -15) = 35225

Calculate the square root of the right side: 187.683243791

Break this problem into two subproblems by setting 
(x + -15) equal to 187.683243791 and -187.683243791.


Subproblem 1
x + -15 = 187.683243791

Simplifying
x + -15 = 187.683243791

Reorder the terms:
-15 + x = 187.683243791

Solving
-15 + x = 187.683243791

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + x = 187.683243791 + 15

Combine like terms: -15 + 15 = 0
0 + x = 187.683243791 + 15
x = 187.683243791 + 15

Combine like terms: 187.683243791 + 15 = 202.683243791
x = 202.683243791

Simplifying
x = 202.683243791


Subproblem 2
x + -15 = -187.683243791

Simplifying
x + -15 = -187.683243791

Reorder the terms:
-15 + x = -187.683243791

Solving
-15 + x = -187.683243791

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + x = -187.683243791 + 15

Combine like terms: -15 + 15 = 0
0 + x = -187.683243791 + 15
x = -187.683243791 + 15

Combine like terms: -187.683243791 + 15 = -172.683243791
x = -172.683243791

Simplifying
x = -172.683243791


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {202.683243791, -172.683243791}

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