5(x^2+45x+13)=0

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Solution for 5(x^2+45x+13)=0 equation:


Simplifying
5(x2 + 45x + 13) = 0

Reorder the terms:
5(13 + 45x + x2) = 0
(13 * 5 + 45x * 5 + x2 * 5) = 0
(65 + 225x + 5x2) = 0

Solving
65 + 225x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(13 + 45x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(13 + 45x + x2)' equal to zero and attempt to solve:

Simplifying
13 + 45x + x2 = 0

Solving
13 + 45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 45x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + 45x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 45x + x2 = 0 + -13
45x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
45x + x2 = -13

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = -13 + 506.25

Reorder the terms:
506.25 + 45x + x2 = -13 + 506.25

Combine like terms: -13 + 506.25 = 493.25
506.25 + 45x + x2 = 493.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 493.25

Calculate the square root of the right side: 22.209232315

Break this problem into two subproblems by setting 
(x + 22.5) equal to 22.209232315 and -22.209232315.


Subproblem 1
x + 22.5 = 22.209232315

Simplifying
x + 22.5 = 22.209232315

Reorder the terms:
22.5 + x = 22.209232315

Solving
22.5 + x = 22.209232315

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 22.209232315 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 22.209232315 + -22.5
x = 22.209232315 + -22.5

Combine like terms: 22.209232315 + -22.5 = -0.290767685
x = -0.290767685

Simplifying
x = -0.290767685


Subproblem 2
x + 22.5 = -22.209232315

Simplifying
x + 22.5 = -22.209232315

Reorder the terms:
22.5 + x = -22.209232315

Solving
22.5 + x = -22.209232315

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -22.209232315 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -22.209232315 + -22.5
x = -22.209232315 + -22.5

Combine like terms: -22.209232315 + -22.5 = -44.709232315
x = -44.709232315

Simplifying
x = -44.709232315


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.290767685, -44.709232315}
Solution
x = {-0.290767685, -44.709232315}

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