Basic Math Examples

${(y - 5)}^{2} = 2 y^{2} - 14 y + 13$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 y^{2} - 14 y + 13 = {(y - 5)}^{2}$

Step 2

Simplify ${(y - 5)}^{2}$ .

Tap for more steps...

Step 2.1

Rewrite.

$2 y^{2} - 14 y + 13 = 0 + 0 + {(y - 5)}^{2}$

Step 2.2

Rewrite ${(y - 5)}^{2}$ as $(y - 5) (y - 5)$ .

$2 y^{2} - 14 y + 13 = (y - 5) (y - 5)$

Step 2.3

Expand $(y - 5) (y - 5)$ using the FOIL Method.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$2 y^{2} - 14 y + 13 = y (y - 5) - 5 (y - 5)$

Step 2.3.2

Apply the distributive property.

$2 y^{2} - 14 y + 13 = y \cdot y + y \cdot - 5 - 5 (y - 5)$

Step 2.3.3

Apply the distributive property.

$2 y^{2} - 14 y + 13 = y \cdot y + y \cdot - 5 - 5 y - 5 \cdot - 5$

Step 2.4

Simplify and combine like terms.

Tap for more steps...

Step 2.4.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1

Multiply $y$ by $y$ .

$2 y^{2} - 14 y + 13 = y^{2} + y \cdot - 5 - 5 y - 5 \cdot - 5$

Step 2.4.1.2

Move $- 5$ to the left of $y$ .

$2 y^{2} - 14 y + 13 = y^{2} - 5 \cdot y - 5 y - 5 \cdot - 5$

Step 2.4.1.3

Multiply $- 5$ by $- 5$ .

$2 y^{2} - 14 y + 13 = y^{2} - 5 y - 5 y + 25$

Step 2.4.2

Subtract $5 y$ from $- 5 y$ .

$2 y^{2} - 14 y + 13 = y^{2} - 10 y + 25$

Step 3

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $y^{2}$ from both sides of the equation.

$2 y^{2} - 14 y + 13 - y^{2} = - 10 y + 25$

Step 3.2

Add $10 y$ to both sides of the equation.

$2 y^{2} - 14 y + 13 - y^{2} + 10 y = 25$

Step 3.3

Subtract $y^{2}$ from $2 y^{2}$ .

$y^{2} - 14 y + 13 + 10 y = 25$

Step 3.4

Add $- 14 y$ and $10 y$ .

$y^{2} - 4 y + 13 = 25$

Step 4

Subtract $25$ from both sides of the equation.

$y^{2} - 4 y + 13 - 25 = 0$

Step 5

Subtract $25$ from $13$ .

$y^{2} - 4 y - 12 = 0$

Step 6

Factor $y^{2} - 4 y - 12$ using the AC method.

Tap for more steps...

Step 6.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $- 4$ .

$- 6, 2$

Step 6.2

Write the factored form using these integers.

$(y - 6) (y + 2) = 0$

Step 7

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

$y - 6 = 0$

$y + 2 = 0$

Step 8

Set $y - 6$ equal to $0$ and solve for $y$ .

Tap for more steps...

Step 8.1

Set $y - 6$ equal to $0$ .

$y - 6 = 0$

Step 8.2

Add $6$ to both sides of the equation.

$y = 6$

Step 9

Set $y + 2$ equal to $0$ and solve for $y$ .

Tap for more steps...

Step 9.1

Set $y + 2$ equal to $0$ .

$y + 2 = 0$

Step 9.2

Subtract $2$ from both sides of the equation.

$y = - 2$

Step 10

The final solution is all the values that make $(y - 6) (y + 2) = 0$ true.

$y = 6, - 2$