25x^2-4x-74=0

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Solution for 25x^2-4x-74=0 equation: 


Simplifying
25x2 + -4x + -74 = 0

Reorder the terms:
-74 + -4x + 25x2 = 0

Solving
-74 + -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'.
-2.96 + -0.16x + x2 = 0

Move the constant term to the right:

Add '2.96' to each side of the equation.
-2.96 + -0.16x + 2.96 + x2 = 0 + 2.96

Reorder the terms:
-2.96 + 2.96 + -0.16x + x2 = 0 + 2.96

Combine like terms: -2.96 + 2.96 = 0.00
0.00 + -0.16x + x2 = 0 + 2.96
-0.16x + x2 = 0 + 2.96

Combine like terms: 0 + 2.96 = 2.96
-0.16x + x2 = 2.96

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 = 2.96 + 0.0064

Reorder the terms:
0.0064 + -0.16x + x2 = 2.96 + 0.0064

Combine like terms: 2.96 + 0.0064 = 2.9664
0.0064 + -0.16x + x2 = 2.9664

Factor a perfect square on the left side:
(x + -0.08)(x + -0.08) = 2.9664

Calculate the square root of the right side: 1.722324011

Break this problem into two subproblems by setting 
(x + -0.08) equal to 1.722324011 and -1.722324011.


Subproblem 1
x + -0.08 = 1.722324011

Simplifying
x + -0.08 = 1.722324011

Reorder the terms:
-0.08 + x = 1.722324011

Solving
-0.08 + x = 1.722324011

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 = 1.722324011 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + x = 1.722324011 + 0.08
x = 1.722324011 + 0.08

Combine like terms: 1.722324011 + 0.08 = 1.802324011
x = 1.802324011

Simplifying
x = 1.802324011


Subproblem 2
x + -0.08 = -1.722324011

Simplifying
x + -0.08 = -1.722324011

Reorder the terms:
-0.08 + x = -1.722324011

Solving
-0.08 + x = -1.722324011

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 = -1.722324011 + 0.08

Combine like terms: -0.08 + 0.08 = 0.00
0.00 + x = -1.722324011 + 0.08
x = -1.722324011 + 0.08

Combine like terms: -1.722324011 + 0.08 = -1.642324011
x = -1.642324011

Simplifying
x = -1.642324011


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.802324011, -1.642324011}

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