7x^2+36x+8=0

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Solution for 7x^2+36x+8=0 equation: 


Simplifying
7x2 + 36x + 8 = 0

Reorder the terms:
8 + 36x + 7x2 = 0

Solving
8 + 36x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
1.142857143 + 5.142857143x + x2 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + 5.142857143x + -1.142857143 + x2 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + 5.142857143x + x2 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + 5.142857143x + x2 = 0 + -1.142857143
5.142857143x + x2 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
5.142857143x + x2 = -1.142857143

The x term is 5.142857143x.  Take half its coefficient (2.571428572).
Square it (6.612244901) and add it to both sides.

Add '6.612244901' to each side of the equation.
5.142857143x + 6.612244901 + x2 = -1.142857143 + 6.612244901

Reorder the terms:
6.612244901 + 5.142857143x + x2 = -1.142857143 + 6.612244901

Combine like terms: -1.142857143 + 6.612244901 = 5.469387758
6.612244901 + 5.142857143x + x2 = 5.469387758

Factor a perfect square on the left side:
(x + 2.571428572)(x + 2.571428572) = 5.469387758

Calculate the square root of the right side: 2.338672221

Break this problem into two subproblems by setting 
(x + 2.571428572) equal to 2.338672221 and -2.338672221.


Subproblem 1
x + 2.571428572 = 2.338672221

Simplifying
x + 2.571428572 = 2.338672221

Reorder the terms:
2.571428572 + x = 2.338672221

Solving
2.571428572 + x = 2.338672221

Solving for variable 'x'.

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

Add '-2.571428572' to each side of the equation.
2.571428572 + -2.571428572 + x = 2.338672221 + -2.571428572

Combine like terms: 2.571428572 + -2.571428572 = 0.000000000
0.000000000 + x = 2.338672221 + -2.571428572
x = 2.338672221 + -2.571428572

Combine like terms: 2.338672221 + -2.571428572 = -0.232756351
x = -0.232756351

Simplifying
x = -0.232756351


Subproblem 2
x + 2.571428572 = -2.338672221

Simplifying
x + 2.571428572 = -2.338672221

Reorder the terms:
2.571428572 + x = -2.338672221

Solving
2.571428572 + x = -2.338672221

Solving for variable 'x'.

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

Add '-2.571428572' to each side of the equation.
2.571428572 + -2.571428572 + x = -2.338672221 + -2.571428572

Combine like terms: 2.571428572 + -2.571428572 = 0.000000000
0.000000000 + x = -2.338672221 + -2.571428572
x = -2.338672221 + -2.571428572

Combine like terms: -2.338672221 + -2.571428572 = -4.910100793
x = -4.910100793

Simplifying
x = -4.910100793


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.232756351, -4.910100793}

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