25x^2+45x-4225=0

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Solution for 25x^2+45x-4225=0 equation: 


Simplifying
25x2 + 45x + -4225 = 0

Reorder the terms:
-4225 + 45x + 25x2 = 0

Solving
-4225 + 45x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-845 + 9x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-845 + 9x + 5x2)' equal to zero and attempt to solve:

Simplifying
-845 + 9x + 5x2 = 0

Solving
-845 + 9x + 5x2 = 0

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

Divide each side by '5'.
-169 + 1.8x + x2 = 0

Move the constant term to the right:

Add '169' to each side of the equation.
-169 + 1.8x + 169 + x2 = 0 + 169

Reorder the terms:
-169 + 169 + 1.8x + x2 = 0 + 169

Combine like terms: -169 + 169 = 0
0 + 1.8x + x2 = 0 + 169
1.8x + x2 = 0 + 169

Combine like terms: 0 + 169 = 169
1.8x + x2 = 169

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 169 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 169 + 0.81

Combine like terms: 169 + 0.81 = 169.81
0.81 + 1.8x + x2 = 169.81

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 169.81

Calculate the square root of the right side: 13.031116606

Break this problem into two subproblems by setting 
(x + 0.9) equal to 13.031116606 and -13.031116606.


Subproblem 1
x + 0.9 = 13.031116606

Simplifying
x + 0.9 = 13.031116606

Reorder the terms:
0.9 + x = 13.031116606

Solving
0.9 + x = 13.031116606

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 13.031116606 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 13.031116606 + -0.9
x = 13.031116606 + -0.9

Combine like terms: 13.031116606 + -0.9 = 12.131116606
x = 12.131116606

Simplifying
x = 12.131116606


Subproblem 2
x + 0.9 = -13.031116606

Simplifying
x + 0.9 = -13.031116606

Reorder the terms:
0.9 + x = -13.031116606

Solving
0.9 + x = -13.031116606

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -13.031116606 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -13.031116606 + -0.9
x = -13.031116606 + -0.9

Combine like terms: -13.031116606 + -0.9 = -13.931116606
x = -13.931116606

Simplifying
x = -13.931116606


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.131116606, -13.931116606}
Solution
x = {12.131116606, -13.931116606}

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