Pre-Algebra Examples

$- x^{2} + 7 x - 10 = 0$

Step 1

Factor the left side of the equation.

Tap for more steps...

Step 1.1

Factor $- 1$ out of $- x^{2} + 7 x - 10$ .

Tap for more steps...

Step 1.1.1

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 7 x - 10 = 0$

Step 1.1.2

Factor $- 1$ out of $7 x$ .

$- (x^{2}) - (- 7 x) - 10 = 0$

Step 1.1.3

Rewrite $- 10$ as $- 1 (10)$ .

$- (x^{2}) - (- 7 x) - 1 \cdot 10 = 0$

Step 1.1.4

Factor $- 1$ out of $- (x^{2}) - (- 7 x)$ .

$- (x^{2} - 7 x) - 1 \cdot 10 = 0$

Step 1.1.5

Factor $- 1$ out of $- (x^{2} - 7 x) - 1 (10)$ .

$- (x^{2} - 7 x + 10) = 0$

Step 1.2

Factor.

Tap for more steps...

Step 1.2.1

Factor $x^{2} - 7 x + 10$ using the AC method.

Tap for more steps...

Step 1.2.1.1

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 $10$ and whose sum is $- 7$ .

$- 5, - 2$

Step 1.2.1.2

Write the factored form using these integers.

$- ((x - 5) (x - 2)) = 0$

Step 1.2.2

Remove unnecessary parentheses.

$- (x - 5) (x - 2) = 0$

Step 2

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

$x - 5 = 0$

$x - 2 = 0$

Step 3

Set $x - 5$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 3.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 3.2

Add $5$ to both sides of the equation.

$x = 5$

Step 4

Set $x - 2$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 4.2

Add $2$ to both sides of the equation.

$x = 2$

Step 5

The final solution is all the values that make $- (x - 5) (x - 2) = 0$ true.

$x = 5, 2$