x^2+54x+75=0

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Solution for x^2+54x+75=0 equation: 


Simplifying
x2 + 54x + 75 = 0

Reorder the terms:
75 + 54x + x2 = 0

Solving
75 + 54x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + 54x + -75 + x2 = 0 + -75

Reorder the terms:
75 + -75 + 54x + x2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + 54x + x2 = 0 + -75
54x + x2 = 0 + -75

Combine like terms: 0 + -75 = -75
54x + x2 = -75

The x term is 54x.  Take half its coefficient (27).
Square it (729) and add it to both sides.

Add '729' to each side of the equation.
54x + 729 + x2 = -75 + 729

Reorder the terms:
729 + 54x + x2 = -75 + 729

Combine like terms: -75 + 729 = 654
729 + 54x + x2 = 654

Factor a perfect square on the left side:
(x + 27)(x + 27) = 654

Calculate the square root of the right side: 25.573423705

Break this problem into two subproblems by setting 
(x + 27) equal to 25.573423705 and -25.573423705.


Subproblem 1
x + 27 = 25.573423705

Simplifying
x + 27 = 25.573423705

Reorder the terms:
27 + x = 25.573423705

Solving
27 + x = 25.573423705

Solving for variable 'x'.

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

Add '-27' to each side of the equation.
27 + -27 + x = 25.573423705 + -27

Combine like terms: 27 + -27 = 0
0 + x = 25.573423705 + -27
x = 25.573423705 + -27

Combine like terms: 25.573423705 + -27 = -1.426576295
x = -1.426576295

Simplifying
x = -1.426576295


Subproblem 2
x + 27 = -25.573423705

Simplifying
x + 27 = -25.573423705

Reorder the terms:
27 + x = -25.573423705

Solving
27 + x = -25.573423705

Solving for variable 'x'.

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

Add '-27' to each side of the equation.
27 + -27 + x = -25.573423705 + -27

Combine like terms: 27 + -27 = 0
0 + x = -25.573423705 + -27
x = -25.573423705 + -27

Combine like terms: -25.573423705 + -27 = -52.573423705
x = -52.573423705

Simplifying
x = -52.573423705


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.426576295, -52.573423705}

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