0.09x^2-6x-5000=0

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Solution for 0.09x^2-6x-5000=0 equation: 


Simplifying
0.09x2 + -6x + -5000 = 0

Reorder the terms:
-5000 + -6x + 0.09x2 = 0

Solving
-5000 + -6x + 0.09x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.09'.
-55555.55556 + -66.66666667x + x2 = 0

Move the constant term to the right:

Add '55555.55556' to each side of the equation.
-55555.55556 + -66.66666667x + 55555.55556 + x2 = 0 + 55555.55556

Reorder the terms:
-55555.55556 + 55555.55556 + -66.66666667x + x2 = 0 + 55555.55556

Combine like terms: -55555.55556 + 55555.55556 = 0.00000
0.00000 + -66.66666667x + x2 = 0 + 55555.55556
-66.66666667x + x2 = 0 + 55555.55556

Combine like terms: 0 + 55555.55556 = 55555.55556
-66.66666667x + x2 = 55555.55556

The x term is -66.66666667x.  Take half its coefficient (-33.33333334).
Square it (1111.111112) and add it to both sides.

Add '1111.111112' to each side of the equation.
-66.66666667x + 1111.111112 + x2 = 55555.55556 + 1111.111112

Reorder the terms:
1111.111112 + -66.66666667x + x2 = 55555.55556 + 1111.111112

Combine like terms: 55555.55556 + 1111.111112 = 56666.666672
1111.111112 + -66.66666667x + x2 = 56666.666672

Factor a perfect square on the left side:
(x + -33.33333334)(x + -33.33333334) = 56666.666672

Calculate the square root of the right side: 238.047614296

Break this problem into two subproblems by setting 
(x + -33.33333334) equal to 238.047614296 and -238.047614296.


Subproblem 1
x + -33.33333334 = 238.047614296

Simplifying
x + -33.33333334 = 238.047614296

Reorder the terms:
-33.33333334 + x = 238.047614296

Solving
-33.33333334 + x = 238.047614296

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = 238.047614296 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = 238.047614296 + 33.33333334
x = 238.047614296 + 33.33333334

Combine like terms: 238.047614296 + 33.33333334 = 271.380947636
x = 271.380947636

Simplifying
x = 271.380947636


Subproblem 2
x + -33.33333334 = -238.047614296

Simplifying
x + -33.33333334 = -238.047614296

Reorder the terms:
-33.33333334 + x = -238.047614296

Solving
-33.33333334 + x = -238.047614296

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = -238.047614296 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = -238.047614296 + 33.33333334
x = -238.047614296 + 33.33333334

Combine like terms: -238.047614296 + 33.33333334 = -204.714280956
x = -204.714280956

Simplifying
x = -204.714280956


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {271.380947636, -204.714280956}

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