25x^2-18x-200=0

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Solution for 25x^2-18x-200=0 equation: 


Simplifying
25x2 + -18x + -200 = 0

Reorder the terms:
-200 + -18x + 25x2 = 0

Solving
-200 + -18x + 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'.
-8 + -0.72x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -0.72x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -0.72x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -0.72x + x2 = 0 + 8
-0.72x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-0.72x + x2 = 8

The x term is -0.72x.  Take half its coefficient (-0.36).
Square it (0.1296) and add it to both sides.

Add '0.1296' to each side of the equation.
-0.72x + 0.1296 + x2 = 8 + 0.1296

Reorder the terms:
0.1296 + -0.72x + x2 = 8 + 0.1296

Combine like terms: 8 + 0.1296 = 8.1296
0.1296 + -0.72x + x2 = 8.1296

Factor a perfect square on the left side:
(x + -0.36)(x + -0.36) = 8.1296

Calculate the square root of the right side: 2.851245342

Break this problem into two subproblems by setting 
(x + -0.36) equal to 2.851245342 and -2.851245342.


Subproblem 1
x + -0.36 = 2.851245342

Simplifying
x + -0.36 = 2.851245342

Reorder the terms:
-0.36 + x = 2.851245342

Solving
-0.36 + x = 2.851245342

Solving for variable 'x'.

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

Add '0.36' to each side of the equation.
-0.36 + 0.36 + x = 2.851245342 + 0.36

Combine like terms: -0.36 + 0.36 = 0.00
0.00 + x = 2.851245342 + 0.36
x = 2.851245342 + 0.36

Combine like terms: 2.851245342 + 0.36 = 3.211245342
x = 3.211245342

Simplifying
x = 3.211245342


Subproblem 2
x + -0.36 = -2.851245342

Simplifying
x + -0.36 = -2.851245342

Reorder the terms:
-0.36 + x = -2.851245342

Solving
-0.36 + x = -2.851245342

Solving for variable 'x'.

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

Add '0.36' to each side of the equation.
-0.36 + 0.36 + x = -2.851245342 + 0.36

Combine like terms: -0.36 + 0.36 = 0.00
0.00 + x = -2.851245342 + 0.36
x = -2.851245342 + 0.36

Combine like terms: -2.851245342 + 0.36 = -2.491245342
x = -2.491245342

Simplifying
x = -2.491245342


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.211245342, -2.491245342}

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