Basic Math Examples

y^{2} + 11 y - 42 = 0

$y^{2} + 11 y - 42 = 0$

Step 1

Factor

y^{2} + 11 y - 42

$y^{2} + 11 y - 42$ using the AC method.

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Step 1.1

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

- 42

$- 42$ and whose sum is

11

$11$ .

- 3, 14

$- 3, 14$

Step 1.2

Write the factored form using these integers.

(y - 3) (y + 14) = 0

$(y - 3) (y + 14) = 0$

(y - 3) (y + 14) = 0

$(y - 3) (y + 14) = 0$

Step 2

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 - 3 = 0

$y - 3 = 0$

y + 14 = 0

$y + 14 = 0$

Step 3

Set

y - 3

$y - 3$ equal to

0

$0$ and solve for

y

$y$ .

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Step 3.1

Set

y - 3

$y - 3$ equal to

0

$0$ .

y - 3 = 0

$y - 3 = 0$

Step 3.2

Add

3

$3$ to both sides of the equation.

y = 3

$y = 3$

y = 3

$y = 3$

Step 4

Set

y + 14

$y + 14$ equal to

0

$0$ and solve for

y

$y$ .

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Step 4.1

Set

y + 14

$y + 14$ equal to

0

$0$ .

y + 14 = 0

$y + 14 = 0$

Step 4.2

Subtract

14

$14$ from both sides of the equation.

y = - 14

$y = - 14$

y = - 14

$y = - 14$

Step 5

The final solution is all the values that make

(y - 3) (y + 14) = 0

$(y - 3) (y + 14) = 0$ true.

y = 3, - 14

$y = 3, - 14$