34x^2-16x+22=0

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Solution for 34x^2-16x+22=0 equation: 


Simplifying
34x2 + -16x + 22 = 0

Reorder the terms:
22 + -16x + 34x2 = 0

Solving
22 + -16x + 34x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + -8x + 17x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + -8x + 17x2)' equal to zero and attempt to solve:

Simplifying
11 + -8x + 17x2 = 0

Solving
11 + -8x + 17x2 = 0

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

Divide each side by '17'.
0.6470588235 + -0.4705882353x + x2 = 0

Move the constant term to the right:

Add '-0.6470588235' to each side of the equation.
0.6470588235 + -0.4705882353x + -0.6470588235 + x2 = 0 + -0.6470588235

Reorder the terms:
0.6470588235 + -0.6470588235 + -0.4705882353x + x2 = 0 + -0.6470588235

Combine like terms: 0.6470588235 + -0.6470588235 = 0.0000000000
0.0000000000 + -0.4705882353x + x2 = 0 + -0.6470588235
-0.4705882353x + x2 = 0 + -0.6470588235

Combine like terms: 0 + -0.6470588235 = -0.6470588235
-0.4705882353x + x2 = -0.6470588235

The x term is -0.4705882353x.  Take half its coefficient (-0.2352941177).
Square it (0.05536332182) and add it to both sides.

Add '0.05536332182' to each side of the equation.
-0.4705882353x + 0.05536332182 + x2 = -0.6470588235 + 0.05536332182

Reorder the terms:
0.05536332182 + -0.4705882353x + x2 = -0.6470588235 + 0.05536332182

Combine like terms: -0.6470588235 + 0.05536332182 = -0.59169550168
0.05536332182 + -0.4705882353x + x2 = -0.59169550168

Factor a perfect square on the left side:
(x + -0.2352941177)(x + -0.2352941177) = -0.59169550168

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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