36x^2-60x-25=

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Solution for 36x^2-60x-25= equation: 


Simplifying
36x2 + -60x + -25 = 0

Reorder the terms:
-25 + -60x + 36x2 = 0

Solving
-25 + -60x + 36x2 = 0

Solving for variable 'x'.

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

Divide each side by '36'.
-0.6944444444 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6944444444' to each side of the equation.
-0.6944444444 + -1.666666667x + 0.6944444444 + x2 = 0 + 0.6944444444

Reorder the terms:
-0.6944444444 + 0.6944444444 + -1.666666667x + x2 = 0 + 0.6944444444

Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000
0.0000000000 + -1.666666667x + x2 = 0 + 0.6944444444
-1.666666667x + x2 = 0 + 0.6944444444

Combine like terms: 0 + 0.6944444444 = 0.6944444444
-1.666666667x + x2 = 0.6944444444

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 0.6944444444 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 0.6944444444 + 0.6944444447

Combine like terms: 0.6944444444 + 0.6944444447 = 1.3888888891
0.6944444447 + -1.666666667x + x2 = 1.3888888891

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 1.3888888891

Calculate the square root of the right side: 1.178511302

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.178511302 and -1.178511302.


Subproblem 1
x + -0.8333333335 = 1.178511302

Simplifying
x + -0.8333333335 = 1.178511302

Reorder the terms:
-0.8333333335 + x = 1.178511302

Solving
-0.8333333335 + x = 1.178511302

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.178511302 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.178511302 + 0.8333333335
x = 1.178511302 + 0.8333333335

Combine like terms: 1.178511302 + 0.8333333335 = 2.0118446355
x = 2.0118446355

Simplifying
x = 2.0118446355


Subproblem 2
x + -0.8333333335 = -1.178511302

Simplifying
x + -0.8333333335 = -1.178511302

Reorder the terms:
-0.8333333335 + x = -1.178511302

Solving
-0.8333333335 + x = -1.178511302

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.178511302 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.178511302 + 0.8333333335
x = -1.178511302 + 0.8333333335

Combine like terms: -1.178511302 + 0.8333333335 = -0.3451779685
x = -0.3451779685

Simplifying
x = -0.3451779685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0118446355, -0.3451779685}

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