4x^2+36x+324=274

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Solution for 4x^2+36x+324=274 equation: 


Simplifying
4x2 + 36x + 324 = 274

Reorder the terms:
324 + 36x + 4x2 = 274

Solving
324 + 36x + 4x2 = 274

Solving for variable 'x'.

Reorder the terms:
324 + -274 + 36x + 4x2 = 274 + -274

Combine like terms: 324 + -274 = 50
50 + 36x + 4x2 = 274 + -274

Combine like terms: 274 + -274 = 0
50 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 18x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 18x + 2x2)' equal to zero and attempt to solve:

Simplifying
25 + 18x + 2x2 = 0

Solving
25 + 18x + 2x2 = 0

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

Divide each side by '2'.
12.5 + 9x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + 9x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + 9x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + 9x + x2 = 0 + -12.5
9x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
9x + x2 = -12.5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -12.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -12.5 + 20.25

Combine like terms: -12.5 + 20.25 = 7.75
20.25 + 9x + x2 = 7.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + 4.5) equal to 2.783882181 and -2.783882181.


Subproblem 1
x + 4.5 = 2.783882181

Simplifying
x + 4.5 = 2.783882181

Reorder the terms:
4.5 + x = 2.783882181

Solving
4.5 + x = 2.783882181

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 2.783882181 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 2.783882181 + -4.5
x = 2.783882181 + -4.5

Combine like terms: 2.783882181 + -4.5 = -1.716117819
x = -1.716117819

Simplifying
x = -1.716117819


Subproblem 2
x + 4.5 = -2.783882181

Simplifying
x + 4.5 = -2.783882181

Reorder the terms:
4.5 + x = -2.783882181

Solving
4.5 + x = -2.783882181

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -2.783882181 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -2.783882181 + -4.5
x = -2.783882181 + -4.5

Combine like terms: -2.783882181 + -4.5 = -7.283882181
x = -7.283882181

Simplifying
x = -7.283882181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.716117819, -7.283882181}
Solution
x = {-1.716117819, -7.283882181}

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