3x^2=5x-8

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Solution for 3x^2=5x-8 equation: 


Simplifying
3x2 = 5x + -8

Reorder the terms:
3x2 = -8 + 5x

Solving
3x2 = -8 + 5x

Solving for variable 'x'.

Reorder the terms:
8 + -5x + 3x2 = -8 + 5x + 8 + -5x

Reorder the terms:
8 + -5x + 3x2 = -8 + 8 + 5x + -5x

Combine like terms: -8 + 8 = 0
8 + -5x + 3x2 = 0 + 5x + -5x
8 + -5x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
8 + -5x + 3x2 = 0

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

Divide each side by '3'.
2.666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -1.666666667x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -1.666666667x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + -2.666666667
-1.666666667x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-1.666666667x + x2 = -2.666666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -2.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -2.666666667 + 0.6944444447

Combine like terms: -2.666666667 + 0.6944444447 = -1.9722222223
0.6944444447 + -1.666666667x + x2 = -1.9722222223

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -1.9722222223

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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