-4x^2+9x-1=0

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Solution for -4x^2+9x-1=0 equation: 


Simplifying
-4x2 + 9x + -1 = 0

Reorder the terms:
-1 + 9x + -4x2 = 0

Solving
-1 + 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'.
0.25 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2.25x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2.25x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2.25x + x2 = 0 + -0.25
-2.25x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2.25x + x2 = -0.25

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 = -0.25 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.25 + 1.265625

Combine like terms: -0.25 + 1.265625 = 1.015625
1.265625 + -2.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.007782219 and -1.007782219.


Subproblem 1
x + -1.125 = 1.007782219

Simplifying
x + -1.125 = 1.007782219

Reorder the terms:
-1.125 + x = 1.007782219

Solving
-1.125 + x = 1.007782219

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 = 1.007782219 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 1.007782219 + 1.125
x = 1.007782219 + 1.125

Combine like terms: 1.007782219 + 1.125 = 2.132782219
x = 2.132782219

Simplifying
x = 2.132782219


Subproblem 2
x + -1.125 = -1.007782219

Simplifying
x + -1.125 = -1.007782219

Reorder the terms:
-1.125 + x = -1.007782219

Solving
-1.125 + x = -1.007782219

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 = -1.007782219 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -1.007782219 + 1.125
x = -1.007782219 + 1.125

Combine like terms: -1.007782219 + 1.125 = 0.117217781
x = 0.117217781

Simplifying
x = 0.117217781


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.132782219, 0.117217781}

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