3x^2+7x+4=36

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Solution for 3x^2+7x+4=36 equation: 


Simplifying
3x2 + 7x + 4 = 36

Reorder the terms:
4 + 7x + 3x2 = 36

Solving
4 + 7x + 3x2 = 36

Solving for variable 'x'.

Reorder the terms:
4 + -36 + 7x + 3x2 = 36 + -36

Combine like terms: 4 + -36 = -32
-32 + 7x + 3x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-32 + 7x + 3x2 = 0

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

Divide each side by '3'.
-10.66666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + 2.333333333x + 10.66666667 + x2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + 2.333333333x + x2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + 2.333333333x + x2 = 0 + 10.66666667
2.333333333x + x2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
2.333333333x + x2 = 10.66666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 10.66666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 10.66666667 + 1.361111112

Combine like terms: 10.66666667 + 1.361111112 = 12.027777782
1.361111112 + 2.333333333x + x2 = 12.027777782

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 12.027777782

Calculate the square root of the right side: 3.468108675

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 3.468108675 and -3.468108675.


Subproblem 1
x + 1.166666667 = 3.468108675

Simplifying
x + 1.166666667 = 3.468108675

Reorder the terms:
1.166666667 + x = 3.468108675

Solving
1.166666667 + x = 3.468108675

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 3.468108675 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 3.468108675 + -1.166666667
x = 3.468108675 + -1.166666667

Combine like terms: 3.468108675 + -1.166666667 = 2.301442008
x = 2.301442008

Simplifying
x = 2.301442008


Subproblem 2
x + 1.166666667 = -3.468108675

Simplifying
x + 1.166666667 = -3.468108675

Reorder the terms:
1.166666667 + x = -3.468108675

Solving
1.166666667 + x = -3.468108675

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -3.468108675 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -3.468108675 + -1.166666667
x = -3.468108675 + -1.166666667

Combine like terms: -3.468108675 + -1.166666667 = -4.634775342
x = -4.634775342

Simplifying
x = -4.634775342


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.301442008, -4.634775342}

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