Solve by Factoring 2y^2-13y+11=0

$2 y^{2} - 13 y + 11 = 0$

Step 1

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 11 = 22$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 y$ .

$2 y^{2} - 13 y + 11 = 0$

Rewrite $- 13$ as $- 2$ plus $- 11$

$2 y^{2} + (- 2 - 11) y + 11 = 0$

Apply the distributive property.

$2 y^{2} - 2 y - 11 y + 11 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 y^{2} - 2 y) - 11 y + 11 = 0$

Factor out the greatest common factor (GCF) from each group.

$2 y (y - 1) - 11 (y - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $y - 1$ .

$(y - 1) (2 y - 11) = 0$

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 1 = 0$

$2 y - 11 = 0$

Step 3

Set $y - 1$ equal to $0$ and solve for $y$ .

Set $y - 1$ equal to $0$ .

$y - 1 = 0$

Add $1$ to both sides of the equation.

$y = 1$

Step 4

Set $2 y - 11$ equal to $0$ and solve for $y$ .

Set $2 y - 11$ equal to $0$ .

$2 y - 11 = 0$

Solve $2 y - 11 = 0$ for $y$ .

Add $11$ to both sides of the equation.

$2 y = 11$

Divide each term in $2 y = 11$ by $2$ and simplify.

Divide each term in $2 y = 11$ by $2$ .

$\frac{2 y}{2} = \frac{11}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{11}{2}$

Divide $y$ by $1$ .

$y = \frac{11}{2}$

Step 5

The final solution is all the values that make $(y - 1) (2 y - 11) = 0$ true.

$y = 1, \frac{11}{2}$

Solve by Factoring 2y^2-13y+11=0

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