4X^2-2X+8=2

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Solution for 4X^2-2X+8=2 equation: 


Simplifying
4X2 + -2X + 8 = 2

Reorder the terms:
8 + -2X + 4X2 = 2

Solving
8 + -2X + 4X2 = 2

Solving for variable 'X'.

Reorder the terms:
8 + -2 + -2X + 4X2 = 2 + -2

Combine like terms: 8 + -2 = 6
6 + -2X + 4X2 = 2 + -2

Combine like terms: 2 + -2 = 0
6 + -2X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1X + 2X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -1X + 2X2)' equal to zero and attempt to solve:

Simplifying
3 + -1X + 2X2 = 0

Solving
3 + -1X + 2X2 = 0

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

Divide each side by '2'.
1.5 + -0.5X + X2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5X + -1.5 + X2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5X + X2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5X + X2 = 0 + -1.5
-0.5X + X2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5X + X2 = -1.5

The X term is -0.5X.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5X + 0.0625 + X2 = -1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5X + X2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + -0.5X + X2 = -1.4375

Factor a perfect square on the left side:
(X + -0.25)(X + -0.25) = -1.4375

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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