0.99x^2-3x-60=0

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Solution for 0.99x^2-3x-60=0 equation: 


Simplifying
0.99x2 + -3x + -60 = 0

Reorder the terms:
-60 + -3x + 0.99x2 = 0

Solving
-60 + -3x + 0.99x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.99'.
-60.60606061 + -3.03030303x + x2 = 0

Move the constant term to the right:

Add '60.60606061' to each side of the equation.
-60.60606061 + -3.03030303x + 60.60606061 + x2 = 0 + 60.60606061

Reorder the terms:
-60.60606061 + 60.60606061 + -3.03030303x + x2 = 0 + 60.60606061

Combine like terms: -60.60606061 + 60.60606061 = 0.00000000
0.00000000 + -3.03030303x + x2 = 0 + 60.60606061
-3.03030303x + x2 = 0 + 60.60606061

Combine like terms: 0 + 60.60606061 = 60.60606061
-3.03030303x + x2 = 60.60606061

The x term is -3.03030303x.  Take half its coefficient (-1.515151515).
Square it (2.295684113) and add it to both sides.

Add '2.295684113' to each side of the equation.
-3.03030303x + 2.295684113 + x2 = 60.60606061 + 2.295684113

Reorder the terms:
2.295684113 + -3.03030303x + x2 = 60.60606061 + 2.295684113

Combine like terms: 60.60606061 + 2.295684113 = 62.901744723
2.295684113 + -3.03030303x + x2 = 62.901744723

Factor a perfect square on the left side:
(x + -1.515151515)(x + -1.515151515) = 62.901744723

Calculate the square root of the right side: 7.931062017

Break this problem into two subproblems by setting 
(x + -1.515151515) equal to 7.931062017 and -7.931062017.


Subproblem 1
x + -1.515151515 = 7.931062017

Simplifying
x + -1.515151515 = 7.931062017

Reorder the terms:
-1.515151515 + x = 7.931062017

Solving
-1.515151515 + x = 7.931062017

Solving for variable 'x'.

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

Add '1.515151515' to each side of the equation.
-1.515151515 + 1.515151515 + x = 7.931062017 + 1.515151515

Combine like terms: -1.515151515 + 1.515151515 = 0.000000000
0.000000000 + x = 7.931062017 + 1.515151515
x = 7.931062017 + 1.515151515

Combine like terms: 7.931062017 + 1.515151515 = 9.446213532
x = 9.446213532

Simplifying
x = 9.446213532


Subproblem 2
x + -1.515151515 = -7.931062017

Simplifying
x + -1.515151515 = -7.931062017

Reorder the terms:
-1.515151515 + x = -7.931062017

Solving
-1.515151515 + x = -7.931062017

Solving for variable 'x'.

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

Add '1.515151515' to each side of the equation.
-1.515151515 + 1.515151515 + x = -7.931062017 + 1.515151515

Combine like terms: -1.515151515 + 1.515151515 = 0.000000000
0.000000000 + x = -7.931062017 + 1.515151515
x = -7.931062017 + 1.515151515

Combine like terms: -7.931062017 + 1.515151515 = -6.415910502
x = -6.415910502

Simplifying
x = -6.415910502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.446213532, -6.415910502}

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