3x^2+81x+34=7

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Solution for 3x^2+81x+34=7 equation: 


Simplifying
3x2 + 81x + 34 = 7

Reorder the terms:
34 + 81x + 3x2 = 7

Solving
34 + 81x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
34 + -7 + 81x + 3x2 = 7 + -7

Combine like terms: 34 + -7 = 27
27 + 81x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
27 + 81x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 27x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 27x + x2)' equal to zero and attempt to solve:

Simplifying
9 + 27x + x2 = 0

Solving
9 + 27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 27x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 27x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 27x + x2 = 0 + -9
27x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
27x + x2 = -9

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = -9 + 182.25

Reorder the terms:
182.25 + 27x + x2 = -9 + 182.25

Combine like terms: -9 + 182.25 = 173.25
182.25 + 27x + x2 = 173.25

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 173.25

Calculate the square root of the right side: 13.162446581

Break this problem into two subproblems by setting 
(x + 13.5) equal to 13.162446581 and -13.162446581.


Subproblem 1
x + 13.5 = 13.162446581

Simplifying
x + 13.5 = 13.162446581

Reorder the terms:
13.5 + x = 13.162446581

Solving
13.5 + x = 13.162446581

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = 13.162446581 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = 13.162446581 + -13.5
x = 13.162446581 + -13.5

Combine like terms: 13.162446581 + -13.5 = -0.337553419
x = -0.337553419

Simplifying
x = -0.337553419


Subproblem 2
x + 13.5 = -13.162446581

Simplifying
x + 13.5 = -13.162446581

Reorder the terms:
13.5 + x = -13.162446581

Solving
13.5 + x = -13.162446581

Solving for variable 'x'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + x = -13.162446581 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + x = -13.162446581 + -13.5
x = -13.162446581 + -13.5

Combine like terms: -13.162446581 + -13.5 = -26.662446581
x = -26.662446581

Simplifying
x = -26.662446581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.337553419, -26.662446581}
Solution
x = {-0.337553419, -26.662446581}

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