8x^2-18x+106=0

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Solution for 8x^2-18x+106=0 equation: 


Simplifying
8x2 + -18x + 106 = 0

Reorder the terms:
106 + -18x + 8x2 = 0

Solving
106 + -18x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(53 + -9x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(53 + -9x + 4x2)' equal to zero and attempt to solve:

Simplifying
53 + -9x + 4x2 = 0

Solving
53 + -9x + 4x2 = 0

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

Divide each side by '4'.
13.25 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-13.25' to each side of the equation.
13.25 + -2.25x + -13.25 + x2 = 0 + -13.25

Reorder the terms:
13.25 + -13.25 + -2.25x + x2 = 0 + -13.25

Combine like terms: 13.25 + -13.25 = 0.00
0.00 + -2.25x + x2 = 0 + -13.25
-2.25x + x2 = 0 + -13.25

Combine like terms: 0 + -13.25 = -13.25
-2.25x + x2 = -13.25

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 = -13.25 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -13.25 + 1.265625

Combine like terms: -13.25 + 1.265625 = -11.984375
1.265625 + -2.25x + x2 = -11.984375

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = -11.984375

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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