-16x^2+22x+4.5=0

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Solution for -16x^2+22x+4.5=0 equation: 


Simplifying
-16x2 + 22x + 4.5 = 0

Reorder the terms:
4.5 + 22x + -16x2 = 0

Solving
4.5 + 22x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.28125 + -1.375x + x2 = 0

Move the constant term to the right:

Add '0.28125' to each side of the equation.
-0.28125 + -1.375x + 0.28125 + x2 = 0 + 0.28125

Reorder the terms:
-0.28125 + 0.28125 + -1.375x + x2 = 0 + 0.28125

Combine like terms: -0.28125 + 0.28125 = 0.00000
0.00000 + -1.375x + x2 = 0 + 0.28125
-1.375x + x2 = 0 + 0.28125

Combine like terms: 0 + 0.28125 = 0.28125
-1.375x + x2 = 0.28125

The x term is -1.375x.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x + 0.47265625 + x2 = 0.28125 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x + x2 = 0.28125 + 0.47265625

Combine like terms: 0.28125 + 0.47265625 = 0.75390625
0.47265625 + -1.375x + x2 = 0.75390625

Factor a perfect square on the left side:
(x + -0.6875)(x + -0.6875) = 0.75390625

Calculate the square root of the right side: 0.868277749

Break this problem into two subproblems by setting 
(x + -0.6875) equal to 0.868277749 and -0.868277749.


Subproblem 1
x + -0.6875 = 0.868277749

Simplifying
x + -0.6875 = 0.868277749

Reorder the terms:
-0.6875 + x = 0.868277749

Solving
-0.6875 + x = 0.868277749

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = 0.868277749 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = 0.868277749 + 0.6875
x = 0.868277749 + 0.6875

Combine like terms: 0.868277749 + 0.6875 = 1.555777749
x = 1.555777749

Simplifying
x = 1.555777749


Subproblem 2
x + -0.6875 = -0.868277749

Simplifying
x + -0.6875 = -0.868277749

Reorder the terms:
-0.6875 + x = -0.868277749

Solving
-0.6875 + x = -0.868277749

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = -0.868277749 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = -0.868277749 + 0.6875
x = -0.868277749 + 0.6875

Combine like terms: -0.868277749 + 0.6875 = -0.180777749
x = -0.180777749

Simplifying
x = -0.180777749


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.555777749, -0.180777749}

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