-4x^2-33x+5=0

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Solution for -4x^2-33x+5=0 equation: 


Simplifying
-4x2 + -33x + 5 = 0

Reorder the terms:
5 + -33x + -4x2 = 0

Solving
5 + -33x + -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'.
-1.25 + 8.25x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 8.25x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 8.25x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 8.25x + x2 = 0 + 1.25
8.25x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
8.25x + x2 = 1.25

The x term is 8.25x.  Take half its coefficient (4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
8.25x + 17.015625 + x2 = 1.25 + 17.015625

Reorder the terms:
17.015625 + 8.25x + x2 = 1.25 + 17.015625

Combine like terms: 1.25 + 17.015625 = 18.265625
17.015625 + 8.25x + x2 = 18.265625

Factor a perfect square on the left side:
(x + 4.125)(x + 4.125) = 18.265625

Calculate the square root of the right side: 4.273830249

Break this problem into two subproblems by setting 
(x + 4.125) equal to 4.273830249 and -4.273830249.


Subproblem 1
x + 4.125 = 4.273830249

Simplifying
x + 4.125 = 4.273830249

Reorder the terms:
4.125 + x = 4.273830249

Solving
4.125 + x = 4.273830249

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = 4.273830249 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = 4.273830249 + -4.125
x = 4.273830249 + -4.125

Combine like terms: 4.273830249 + -4.125 = 0.148830249
x = 0.148830249

Simplifying
x = 0.148830249


Subproblem 2
x + 4.125 = -4.273830249

Simplifying
x + 4.125 = -4.273830249

Reorder the terms:
4.125 + x = -4.273830249

Solving
4.125 + x = -4.273830249

Solving for variable 'x'.

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

Add '-4.125' to each side of the equation.
4.125 + -4.125 + x = -4.273830249 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + x = -4.273830249 + -4.125
x = -4.273830249 + -4.125

Combine like terms: -4.273830249 + -4.125 = -8.398830249
x = -8.398830249

Simplifying
x = -8.398830249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.148830249, -8.398830249}

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