5x^2+20x-725=0

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Solution for 5x^2+20x-725=0 equation: 


Simplifying
5x2 + 20x + -725 = 0

Reorder the terms:
-725 + 20x + 5x2 = 0

Solving
-725 + 20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-145 + 4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-145 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-145 + 4x + x2 = 0

Solving
-145 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '145' to each side of the equation.
-145 + 4x + 145 + x2 = 0 + 145

Reorder the terms:
-145 + 145 + 4x + x2 = 0 + 145

Combine like terms: -145 + 145 = 0
0 + 4x + x2 = 0 + 145
4x + x2 = 0 + 145

Combine like terms: 0 + 145 = 145
4x + x2 = 145

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 145 + 4

Reorder the terms:
4 + 4x + x2 = 145 + 4

Combine like terms: 145 + 4 = 149
4 + 4x + x2 = 149

Factor a perfect square on the left side:
(x + 2)(x + 2) = 149

Calculate the square root of the right side: 12.206555616

Break this problem into two subproblems by setting 
(x + 2) equal to 12.206555616 and -12.206555616.


Subproblem 1
x + 2 = 12.206555616

Simplifying
x + 2 = 12.206555616

Reorder the terms:
2 + x = 12.206555616

Solving
2 + x = 12.206555616

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 12.206555616 + -2

Combine like terms: 2 + -2 = 0
0 + x = 12.206555616 + -2
x = 12.206555616 + -2

Combine like terms: 12.206555616 + -2 = 10.206555616
x = 10.206555616

Simplifying
x = 10.206555616


Subproblem 2
x + 2 = -12.206555616

Simplifying
x + 2 = -12.206555616

Reorder the terms:
2 + x = -12.206555616

Solving
2 + x = -12.206555616

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -12.206555616 + -2

Combine like terms: 2 + -2 = 0
0 + x = -12.206555616 + -2
x = -12.206555616 + -2

Combine like terms: -12.206555616 + -2 = -14.206555616
x = -14.206555616

Simplifying
x = -14.206555616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.206555616, -14.206555616}
Solution
x = {10.206555616, -14.206555616}

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