-4x^2-9x+8=0

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Solution for -4x^2-9x+8=0 equation: 


Simplifying
-4x2 + -9x + 8 = 0

Reorder the terms:
8 + -9x + -4x2 = 0

Solving
8 + -9x + -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'.
-2 + 2.25x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.25x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.25x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.25x + x2 = 0 + 2
2.25x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.25x + x2 = 2

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 2 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 2 + 1.265625

Combine like terms: 2 + 1.265625 = 3.265625
1.265625 + 2.25x + x2 = 3.265625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 3.265625

Calculate the square root of the right side: 1.807104037

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.807104037 and -1.807104037.


Subproblem 1
x + 1.125 = 1.807104037

Simplifying
x + 1.125 = 1.807104037

Reorder the terms:
1.125 + x = 1.807104037

Solving
1.125 + x = 1.807104037

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.807104037 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.807104037 + -1.125
x = 1.807104037 + -1.125

Combine like terms: 1.807104037 + -1.125 = 0.682104037
x = 0.682104037

Simplifying
x = 0.682104037


Subproblem 2
x + 1.125 = -1.807104037

Simplifying
x + 1.125 = -1.807104037

Reorder the terms:
1.125 + x = -1.807104037

Solving
1.125 + x = -1.807104037

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.807104037 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.807104037 + -1.125
x = -1.807104037 + -1.125

Combine like terms: -1.807104037 + -1.125 = -2.932104037
x = -2.932104037

Simplifying
x = -2.932104037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.682104037, -2.932104037}

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