5y^2=3y-7

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Solution for 5y^2=3y-7 equation:


Simplifying
5y2 = 3y + -7

Reorder the terms:
5y2 = -7 + 3y

Solving
5y2 = -7 + 3y

Solving for variable 'y'.

Reorder the terms:
7 + -3y + 5y2 = -7 + 3y + 7 + -3y

Reorder the terms:
7 + -3y + 5y2 = -7 + 7 + 3y + -3y

Combine like terms: -7 + 7 = 0
7 + -3y + 5y2 = 0 + 3y + -3y
7 + -3y + 5y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
7 + -3y + 5y2 = 0

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

Divide each side by '5'.
1.4 + -0.6y + y2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + -0.6y + -1.4 + y2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + -0.6y + y2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + -0.6y + y2 = 0 + -1.4
-0.6y + y2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
-0.6y + y2 = -1.4

The y term is -0.6y.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6y + 0.09 + y2 = -1.4 + 0.09

Reorder the terms:
0.09 + -0.6y + y2 = -1.4 + 0.09

Combine like terms: -1.4 + 0.09 = -1.31
0.09 + -0.6y + y2 = -1.31

Factor a perfect square on the left side:
(y + -0.3)(y + -0.3) = -1.31

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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