Algebra Examples

$y = x^{2} - 13 x + 30$

Step 1

Set $x^{2} - 13 x + 30$ equal to $0$ .

$x^{2} - 13 x + 30 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor $x^{2} - 13 x + 30$ using the AC method.

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Step 2.1.1

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 $30$ and whose sum is $- 13$ .

$- 10, - 3$

Step 2.1.2

Write the factored form using these integers.

$(x - 10) (x - 3) = 0$

Step 2.2

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

$x - 10 = 0$

$x - 3 = 0$

Step 2.3

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 2.3.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 2.3.2

Add $10$ to both sides of the equation.

$x = 10$

Step 2.4

Set $x - 3$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Step 2.4.2

Add $3$ to both sides of the equation.

$x = 3$

Step 2.5

The final solution is all the values that make $(x - 10) (x - 3) = 0$ true.

$x = 10, 3$

Step 3