4x^2-22x+42=0

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Solution for 4x^2-22x+42=0 equation: 


Simplifying
4x2 + -22x + 42 = 0

Reorder the terms:
42 + -22x + 4x2 = 0

Solving
42 + -22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -11x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(21 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
21 + -11x + 2x2 = 0

Solving
21 + -11x + 2x2 = 0

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

Divide each side by '2'.
10.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -5.5x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -5.5x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -5.5x + x2 = 0 + -10.5
-5.5x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-5.5x + x2 = -10.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -10.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -10.5 + 7.5625

Combine like terms: -10.5 + 7.5625 = -2.9375
7.5625 + -5.5x + x2 = -2.9375

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = -2.9375

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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