16x^2-24x+22=0

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Solution for 16x^2-24x+22=0 equation: 


Simplifying
16x2 + -24x + 22 = 0

Reorder the terms:
22 + -24x + 16x2 = 0

Solving
22 + -24x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -12x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -12x + 8x2)' equal to zero and attempt to solve:

Simplifying
11 + -12x + 8x2 = 0

Solving
11 + -12x + 8x2 = 0

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

Divide each side by '8'.
1.375 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-1.375' to each side of the equation.
1.375 + -1.5x + -1.375 + x2 = 0 + -1.375

Reorder the terms:
1.375 + -1.375 + -1.5x + x2 = 0 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + -1.5x + x2 = 0 + -1.375
-1.5x + x2 = 0 + -1.375

Combine like terms: 0 + -1.375 = -1.375
-1.5x + x2 = -1.375

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -1.375 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -1.375 + 0.5625

Combine like terms: -1.375 + 0.5625 = -0.8125
0.5625 + -1.5x + x2 = -0.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -0.8125

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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