4x^2-36x+3=0

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Solution for 4x^2-36x+3=0 equation: 


Simplifying
4x2 + -36x + 3 = 0

Reorder the terms:
3 + -36x + 4x2 = 0

Solving
3 + -36x + 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'.
0.75 + -9x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -9x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -9x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -9x + x2 = 0 + -0.75
-9x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-9x + x2 = -0.75

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -0.75 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -0.75 + 20.25

Combine like terms: -0.75 + 20.25 = 19.5
20.25 + -9x + x2 = 19.5

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 19.5

Calculate the square root of the right side: 4.415880433

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.415880433 and -4.415880433.


Subproblem 1
x + -4.5 = 4.415880433

Simplifying
x + -4.5 = 4.415880433

Reorder the terms:
-4.5 + x = 4.415880433

Solving
-4.5 + x = 4.415880433

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.415880433 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.415880433 + 4.5
x = 4.415880433 + 4.5

Combine like terms: 4.415880433 + 4.5 = 8.915880433
x = 8.915880433

Simplifying
x = 8.915880433


Subproblem 2
x + -4.5 = -4.415880433

Simplifying
x + -4.5 = -4.415880433

Reorder the terms:
-4.5 + x = -4.415880433

Solving
-4.5 + x = -4.415880433

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.415880433 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.415880433 + 4.5
x = -4.415880433 + 4.5

Combine like terms: -4.415880433 + 4.5 = 0.084119567
x = 0.084119567

Simplifying
x = 0.084119567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.915880433, 0.084119567}

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