Basic Math Examples

y^{2} + 16 y = - 15

$y^{2} + 16 y = - 15$

Step 1

Add

15

$15$ to both sides of the equation.

y^{2} + 16 y + 15 = 0

$y^{2} + 16 y + 15 = 0$

Step 2

Factor

y^{2} + 16 y + 15

$y^{2} + 16 y + 15$ using the AC method.

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Step 2.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

15

$15$ and whose sum is

16

$16$ .

1, 15

$1, 15$

Step 2.2

Write the factored form using these integers.

(y + 1) (y + 15) = 0

$(y + 1) (y + 15) = 0$

(y + 1) (y + 15) = 0

$(y + 1) (y + 15) = 0$

Step 3

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

y + 1 = 0

$y + 1 = 0$

y + 15 = 0

$y + 15 = 0$

Step 4

Set

y + 1

$y + 1$ equal to

0

$0$ and solve for

y

$y$ .

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Step 4.1

Set

y + 1

$y + 1$ equal to

0

$0$ .

y + 1 = 0

$y + 1 = 0$

Step 4.2

Subtract

1

$1$ from both sides of the equation.

y = - 1

$y = - 1$

y = - 1

$y = - 1$

Step 5

Set

y + 15

$y + 15$ equal to

0

$0$ and solve for

y

$y$ .

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Step 5.1

Set

y + 15

$y + 15$ equal to

0

$0$ .

y + 15 = 0

$y + 15 = 0$

Step 5.2

Subtract

15

$15$ from both sides of the equation.

y = - 15

$y = - 15$

y = - 15

$y = - 15$

Step 6

The final solution is all the values that make

(y + 1) (y + 15) = 0

$(y + 1) (y + 15) = 0$ true.

y = - 1, - 15

$y = - 1, - 15$