3x^2+12x+20=245

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Solution for 3x^2+12x+20=245 equation: 


Simplifying
3x2 + 12x + 20 = 245

Reorder the terms:
20 + 12x + 3x2 = 245

Solving
20 + 12x + 3x2 = 245

Solving for variable 'x'.

Reorder the terms:
20 + -245 + 12x + 3x2 = 245 + -245

Combine like terms: 20 + -245 = -225
-225 + 12x + 3x2 = 245 + -245

Combine like terms: 245 + -245 = 0
-225 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-75 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-75 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + 4x + x2 = 0

Solving
-75 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 4x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 4x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 4x + x2 = 0 + 75
4x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
4x + x2 = 75

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 75 + 4

Reorder the terms:
4 + 4x + x2 = 75 + 4

Combine like terms: 75 + 4 = 79
4 + 4x + x2 = 79

Factor a perfect square on the left side:
(x + 2)(x + 2) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + 2) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + 2 = 8.888194417

Simplifying
x + 2 = 8.888194417

Reorder the terms:
2 + x = 8.888194417

Solving
2 + x = 8.888194417

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 8.888194417 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8.888194417 + -2
x = 8.888194417 + -2

Combine like terms: 8.888194417 + -2 = 6.888194417
x = 6.888194417

Simplifying
x = 6.888194417


Subproblem 2
x + 2 = -8.888194417

Simplifying
x + 2 = -8.888194417

Reorder the terms:
2 + x = -8.888194417

Solving
2 + x = -8.888194417

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -8.888194417 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8.888194417 + -2
x = -8.888194417 + -2

Combine like terms: -8.888194417 + -2 = -10.888194417
x = -10.888194417

Simplifying
x = -10.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.888194417, -10.888194417}
Solution
x = {6.888194417, -10.888194417}

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