25x^2+140x+125=180

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Solution for 25x^2+140x+125=180 equation: 


Simplifying
25x2 + 140x + 125 = 180

Reorder the terms:
125 + 140x + 25x2 = 180

Solving
125 + 140x + 25x2 = 180

Solving for variable 'x'.

Reorder the terms:
125 + -180 + 140x + 25x2 = 180 + -180

Combine like terms: 125 + -180 = -55
-55 + 140x + 25x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-55 + 140x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-11 + 28x + 5x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-11 + 28x + 5x2)' equal to zero and attempt to solve:

Simplifying
-11 + 28x + 5x2 = 0

Solving
-11 + 28x + 5x2 = 0

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

Divide each side by '5'.
-2.2 + 5.6x + x2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 5.6x + 2.2 + x2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 5.6x + x2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 5.6x + x2 = 0 + 2.2
5.6x + x2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
5.6x + x2 = 2.2

The x term is 5.6x.  Take half its coefficient (2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
5.6x + 7.84 + x2 = 2.2 + 7.84

Reorder the terms:
7.84 + 5.6x + x2 = 2.2 + 7.84

Combine like terms: 2.2 + 7.84 = 10.04
7.84 + 5.6x + x2 = 10.04

Factor a perfect square on the left side:
(x + 2.8)(x + 2.8) = 10.04

Calculate the square root of the right side: 3.168595904

Break this problem into two subproblems by setting 
(x + 2.8) equal to 3.168595904 and -3.168595904.


Subproblem 1
x + 2.8 = 3.168595904

Simplifying
x + 2.8 = 3.168595904

Reorder the terms:
2.8 + x = 3.168595904

Solving
2.8 + x = 3.168595904

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = 3.168595904 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = 3.168595904 + -2.8
x = 3.168595904 + -2.8

Combine like terms: 3.168595904 + -2.8 = 0.368595904
x = 0.368595904

Simplifying
x = 0.368595904


Subproblem 2
x + 2.8 = -3.168595904

Simplifying
x + 2.8 = -3.168595904

Reorder the terms:
2.8 + x = -3.168595904

Solving
2.8 + x = -3.168595904

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = -3.168595904 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = -3.168595904 + -2.8
x = -3.168595904 + -2.8

Combine like terms: -3.168595904 + -2.8 = -5.968595904
x = -5.968595904

Simplifying
x = -5.968595904


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.368595904, -5.968595904}
Solution
x = {0.368595904, -5.968595904}

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