25x^2-4x-5625=0

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Solution for 25x^2-4x-5625=0 equation: 


Simplifying
25x2 + -4x + -5625 = 0

Reorder the terms:
-5625 + -4x + 25x2 = 0

Solving
-5625 + -4x + 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'.
-225 + -0.16x + x2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -0.16x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -0.16x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -0.16x + x2 = 0 + 225
-0.16x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-0.16x + x2 = 225

The x term is -0.16x.  Take half its coefficient (-0.08).
Square it (0.0064) and add it to both sides.

Add '0.0064' to each side of the equation.
-0.16x + 0.0064 + x2 = 225 + 0.0064

Reorder the terms:
0.0064 + -0.16x + x2 = 225 + 0.0064

Combine like terms: 225 + 0.0064 = 225.0064
0.0064 + -0.16x + x2 = 225.0064

Factor a perfect square on the left side:
(x + -0.08)(x + -0.08) = 225.0064

Calculate the square root of the right side: 15.000213332

Break this problem into two subproblems by setting 
(x + -0.08) equal to 15.000213332 and -15.000213332.


Subproblem 1
x + -0.08 = 15.000213332

Simplifying
x + -0.08 = 15.000213332

Reorder the terms:
-0.08 + x = 15.000213332

Solving
-0.08 + x = 15.000213332

Solving for variable 'x'.

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

Add '0.08' to each side of the equation.
-0.08 + 0.08 + x = 15.000213332 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + x = 15.000213332 + 0.08
x = 15.000213332 + 0.08

Combine like terms: 15.000213332 + 0.08 = 15.080213332
x = 15.080213332

Simplifying
x = 15.080213332


Subproblem 2
x + -0.08 = -15.000213332

Simplifying
x + -0.08 = -15.000213332

Reorder the terms:
-0.08 + x = -15.000213332

Solving
-0.08 + x = -15.000213332

Solving for variable 'x'.

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

Add '0.08' to each side of the equation.
-0.08 + 0.08 + x = -15.000213332 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + x = -15.000213332 + 0.08
x = -15.000213332 + 0.08

Combine like terms: -15.000213332 + 0.08 = -14.920213332
x = -14.920213332

Simplifying
x = -14.920213332


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.080213332, -14.920213332}

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