1.35x^2-9x-6000=0

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Solution for 1.35x^2-9x-6000=0 equation: 


Simplifying
1.35x2 + -9x + -6000 = 0

Reorder the terms:
-6000 + -9x + 1.35x2 = 0

Solving
-6000 + -9x + 1.35x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.35'.
-4444.444444 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '4444.444444' to each side of the equation.
-4444.444444 + -6.666666667x + 4444.444444 + x2 = 0 + 4444.444444

Reorder the terms:
-4444.444444 + 4444.444444 + -6.666666667x + x2 = 0 + 4444.444444

Combine like terms: -4444.444444 + 4444.444444 = 0.000000
0.000000 + -6.666666667x + x2 = 0 + 4444.444444
-6.666666667x + x2 = 0 + 4444.444444

Combine like terms: 0 + 4444.444444 = 4444.444444
-6.666666667x + x2 = 4444.444444

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 4444.444444 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 4444.444444 + 11.11111112

Combine like terms: 4444.444444 + 11.11111112 = 4455.55555512
11.11111112 + -6.666666667x + x2 = 4455.55555512

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 4455.55555512

Calculate the square root of the right side: 66.749947978

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 66.749947978 and -66.749947978.


Subproblem 1
x + -3.333333334 = 66.749947978

Simplifying
x + -3.333333334 = 66.749947978

Reorder the terms:
-3.333333334 + x = 66.749947978

Solving
-3.333333334 + x = 66.749947978

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 66.749947978 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 66.749947978 + 3.333333334
x = 66.749947978 + 3.333333334

Combine like terms: 66.749947978 + 3.333333334 = 70.083281312
x = 70.083281312

Simplifying
x = 70.083281312


Subproblem 2
x + -3.333333334 = -66.749947978

Simplifying
x + -3.333333334 = -66.749947978

Reorder the terms:
-3.333333334 + x = -66.749947978

Solving
-3.333333334 + x = -66.749947978

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -66.749947978 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -66.749947978 + 3.333333334
x = -66.749947978 + 3.333333334

Combine like terms: -66.749947978 + 3.333333334 = -63.416614644
x = -63.416614644

Simplifying
x = -63.416614644


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {70.083281312, -63.416614644}

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