25x^2-6x-144=0

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Solution for 25x^2-6x-144=0 equation: 


Simplifying
25x2 + -6x + -144 = 0

Reorder the terms:
-144 + -6x + 25x2 = 0

Solving
-144 + -6x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-5.76 + -0.24x + x2 = 0

Move the constant term to the right:

Add '5.76' to each side of the equation.
-5.76 + -0.24x + 5.76 + x2 = 0 + 5.76

Reorder the terms:
-5.76 + 5.76 + -0.24x + x2 = 0 + 5.76

Combine like terms: -5.76 + 5.76 = 0.00
0.00 + -0.24x + x2 = 0 + 5.76
-0.24x + x2 = 0 + 5.76

Combine like terms: 0 + 5.76 = 5.76
-0.24x + x2 = 5.76

The x term is -0.24x.  Take half its coefficient (-0.12).
Square it (0.0144) and add it to both sides.

Add '0.0144' to each side of the equation.
-0.24x + 0.0144 + x2 = 5.76 + 0.0144

Reorder the terms:
0.0144 + -0.24x + x2 = 5.76 + 0.0144

Combine like terms: 5.76 + 0.0144 = 5.7744
0.0144 + -0.24x + x2 = 5.7744

Factor a perfect square on the left side:
(x + -0.12)(x + -0.12) = 5.7744

Calculate the square root of the right side: 2.402998127

Break this problem into two subproblems by setting 
(x + -0.12) equal to 2.402998127 and -2.402998127.


Subproblem 1
x + -0.12 = 2.402998127

Simplifying
x + -0.12 = 2.402998127

Reorder the terms:
-0.12 + x = 2.402998127

Solving
-0.12 + x = 2.402998127

Solving for variable 'x'.

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

Add '0.12' to each side of the equation.
-0.12 + 0.12 + x = 2.402998127 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + x = 2.402998127 + 0.12
x = 2.402998127 + 0.12

Combine like terms: 2.402998127 + 0.12 = 2.522998127
x = 2.522998127

Simplifying
x = 2.522998127


Subproblem 2
x + -0.12 = -2.402998127

Simplifying
x + -0.12 = -2.402998127

Reorder the terms:
-0.12 + x = -2.402998127

Solving
-0.12 + x = -2.402998127

Solving for variable 'x'.

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

Add '0.12' to each side of the equation.
-0.12 + 0.12 + x = -2.402998127 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + x = -2.402998127 + 0.12
x = -2.402998127 + 0.12

Combine like terms: -2.402998127 + 0.12 = -2.282998127
x = -2.282998127

Simplifying
x = -2.282998127


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.522998127, -2.282998127}

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