3x^2+x^2+6x+9=289

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Solution for 3x^2+x^2+6x+9=289 equation: 


Simplifying
3x2 + x2 + 6x + 9 = 289

Reorder the terms:
9 + 6x + 3x2 + x2 = 289

Combine like terms: 3x2 + x2 = 4x2
9 + 6x + 4x2 = 289

Solving
9 + 6x + 4x2 = 289

Solving for variable 'x'.

Reorder the terms:
9 + -289 + 6x + 4x2 = 289 + -289

Combine like terms: 9 + -289 = -280
-280 + 6x + 4x2 = 289 + -289

Combine like terms: 289 + -289 = 0
-280 + 6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-140 + 3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-140 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-140 + 3x + 2x2 = 0

Solving
-140 + 3x + 2x2 = 0

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

Divide each side by '2'.
-70 + 1.5x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 1.5x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 1.5x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 1.5x + x2 = 0 + 70
1.5x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
1.5x + x2 = 70

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 70 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 70 + 0.5625

Combine like terms: 70 + 0.5625 = 70.5625
0.5625 + 1.5x + x2 = 70.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 70.5625

Calculate the square root of the right side: 8.400148808

Break this problem into two subproblems by setting 
(x + 0.75) equal to 8.400148808 and -8.400148808.


Subproblem 1
x + 0.75 = 8.400148808

Simplifying
x + 0.75 = 8.400148808

Reorder the terms:
0.75 + x = 8.400148808

Solving
0.75 + x = 8.400148808

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 8.400148808 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 8.400148808 + -0.75
x = 8.400148808 + -0.75

Combine like terms: 8.400148808 + -0.75 = 7.650148808
x = 7.650148808

Simplifying
x = 7.650148808


Subproblem 2
x + 0.75 = -8.400148808

Simplifying
x + 0.75 = -8.400148808

Reorder the terms:
0.75 + x = -8.400148808

Solving
0.75 + x = -8.400148808

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -8.400148808 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -8.400148808 + -0.75
x = -8.400148808 + -0.75

Combine like terms: -8.400148808 + -0.75 = -9.150148808
x = -9.150148808

Simplifying
x = -9.150148808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.650148808, -9.150148808}
Solution
x = {7.650148808, -9.150148808}

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