0.99x^2-4x-60=0

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Solution for 0.99x^2-4x-60=0 equation: 


Simplifying
0.99x2 + -4x + -60 = 0

Reorder the terms:
-60 + -4x + 0.99x2 = 0

Solving
-60 + -4x + 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 + -4.04040404x + x2 = 0

Move the constant term to the right:

Add '60.60606061' to each side of the equation.
-60.60606061 + -4.04040404x + 60.60606061 + x2 = 0 + 60.60606061

Reorder the terms:
-60.60606061 + 60.60606061 + -4.04040404x + x2 = 0 + 60.60606061

Combine like terms: -60.60606061 + 60.60606061 = 0.00000000
0.00000000 + -4.04040404x + x2 = 0 + 60.60606061
-4.04040404x + x2 = 0 + 60.60606061

Combine like terms: 0 + 60.60606061 = 60.60606061
-4.04040404x + x2 = 60.60606061

The x term is -4.04040404x.  Take half its coefficient (-2.02020202).
Square it (4.081216202) and add it to both sides.

Add '4.081216202' to each side of the equation.
-4.04040404x + 4.081216202 + x2 = 60.60606061 + 4.081216202

Reorder the terms:
4.081216202 + -4.04040404x + x2 = 60.60606061 + 4.081216202

Combine like terms: 60.60606061 + 4.081216202 = 64.687276812
4.081216202 + -4.04040404x + x2 = 64.687276812

Factor a perfect square on the left side:
(x + -2.02020202)(x + -2.02020202) = 64.687276812

Calculate the square root of the right side: 8.042840096

Break this problem into two subproblems by setting 
(x + -2.02020202) equal to 8.042840096 and -8.042840096.


Subproblem 1
x + -2.02020202 = 8.042840096

Simplifying
x + -2.02020202 = 8.042840096

Reorder the terms:
-2.02020202 + x = 8.042840096

Solving
-2.02020202 + x = 8.042840096

Solving for variable 'x'.

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

Add '2.02020202' to each side of the equation.
-2.02020202 + 2.02020202 + x = 8.042840096 + 2.02020202

Combine like terms: -2.02020202 + 2.02020202 = 0.00000000
0.00000000 + x = 8.042840096 + 2.02020202
x = 8.042840096 + 2.02020202

Combine like terms: 8.042840096 + 2.02020202 = 10.063042116
x = 10.063042116

Simplifying
x = 10.063042116


Subproblem 2
x + -2.02020202 = -8.042840096

Simplifying
x + -2.02020202 = -8.042840096

Reorder the terms:
-2.02020202 + x = -8.042840096

Solving
-2.02020202 + x = -8.042840096

Solving for variable 'x'.

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

Add '2.02020202' to each side of the equation.
-2.02020202 + 2.02020202 + x = -8.042840096 + 2.02020202

Combine like terms: -2.02020202 + 2.02020202 = 0.00000000
0.00000000 + x = -8.042840096 + 2.02020202
x = -8.042840096 + 2.02020202

Combine like terms: -8.042840096 + 2.02020202 = -6.022638076
x = -6.022638076

Simplifying
x = -6.022638076


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.063042116, -6.022638076}

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