5(x^2+55x+90)=0

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Solution for 5(x^2+55x+90)=0 equation: 


Simplifying
5(x2 + 55x + 90) = 0

Reorder the terms:
5(90 + 55x + x2) = 0
(90 * 5 + 55x * 5 + x2 * 5) = 0
(450 + 275x + 5x2) = 0

Solving
450 + 275x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(90 + 55x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(90 + 55x + x2)' equal to zero and attempt to solve:

Simplifying
90 + 55x + x2 = 0

Solving
90 + 55x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + 55x + -90 + x2 = 0 + -90

Reorder the terms:
90 + -90 + 55x + x2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + 55x + x2 = 0 + -90
55x + x2 = 0 + -90

Combine like terms: 0 + -90 = -90
55x + x2 = -90

The x term is 55x.  Take half its coefficient (27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
55x + 756.25 + x2 = -90 + 756.25

Reorder the terms:
756.25 + 55x + x2 = -90 + 756.25

Combine like terms: -90 + 756.25 = 666.25
756.25 + 55x + x2 = 666.25

Factor a perfect square on the left side:
(x + 27.5)(x + 27.5) = 666.25

Calculate the square root of the right side: 25.811818998

Break this problem into two subproblems by setting 
(x + 27.5) equal to 25.811818998 and -25.811818998.


Subproblem 1
x + 27.5 = 25.811818998

Simplifying
x + 27.5 = 25.811818998

Reorder the terms:
27.5 + x = 25.811818998

Solving
27.5 + x = 25.811818998

Solving for variable 'x'.

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

Add '-27.5' to each side of the equation.
27.5 + -27.5 + x = 25.811818998 + -27.5

Combine like terms: 27.5 + -27.5 = 0.0
0.0 + x = 25.811818998 + -27.5
x = 25.811818998 + -27.5

Combine like terms: 25.811818998 + -27.5 = -1.688181002
x = -1.688181002

Simplifying
x = -1.688181002


Subproblem 2
x + 27.5 = -25.811818998

Simplifying
x + 27.5 = -25.811818998

Reorder the terms:
27.5 + x = -25.811818998

Solving
27.5 + x = -25.811818998

Solving for variable 'x'.

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

Add '-27.5' to each side of the equation.
27.5 + -27.5 + x = -25.811818998 + -27.5

Combine like terms: 27.5 + -27.5 = 0.0
0.0 + x = -25.811818998 + -27.5
x = -25.811818998 + -27.5

Combine like terms: -25.811818998 + -27.5 = -53.311818998
x = -53.311818998

Simplifying
x = -53.311818998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.688181002, -53.311818998}
Solution
x = {-1.688181002, -53.311818998}

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