4x^2+29x+36=0

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Solution for 4x^2+29x+36=0 equation: 


Simplifying
4x2 + 29x + 36 = 0

Reorder the terms:
36 + 29x + 4x2 = 0

Solving
36 + 29x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
9 + 7.25x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 7.25x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 7.25x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7.25x + x2 = 0 + -9
7.25x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
7.25x + x2 = -9

The x term is 7.25x.  Take half its coefficient (3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
7.25x + 13.140625 + x2 = -9 + 13.140625

Reorder the terms:
13.140625 + 7.25x + x2 = -9 + 13.140625

Combine like terms: -9 + 13.140625 = 4.140625
13.140625 + 7.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + 3.625)(x + 3.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + 3.625) equal to 2.034852575 and -2.034852575.


Subproblem 1
x + 3.625 = 2.034852575

Simplifying
x + 3.625 = 2.034852575

Reorder the terms:
3.625 + x = 2.034852575

Solving
3.625 + x = 2.034852575

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = 2.034852575 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = 2.034852575 + -3.625
x = 2.034852575 + -3.625

Combine like terms: 2.034852575 + -3.625 = -1.590147425
x = -1.590147425

Simplifying
x = -1.590147425


Subproblem 2
x + 3.625 = -2.034852575

Simplifying
x + 3.625 = -2.034852575

Reorder the terms:
3.625 + x = -2.034852575

Solving
3.625 + x = -2.034852575

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = -2.034852575 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = -2.034852575 + -3.625
x = -2.034852575 + -3.625

Combine like terms: -2.034852575 + -3.625 = -5.659852575
x = -5.659852575

Simplifying
x = -5.659852575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.590147425, -5.659852575}

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