Mathway

Visit Mathway on the web

Start 7-day free trial on the app

Start 7-day free trial on the app

Download free on Amazon

Download free in Windows Store

Take a photo of your math problem on the app

Examples

$f (x) = 6 x - 16$ ,

$f (x) = - x^{2}$

Step 1

Substitute

$- x^{2}$ for

$f (x)$ .

$- x^{2} = 6 x - 16$

Step 2

Solve for

$x$ .

Tap for more steps...

Step 2.1

Subtract

$6 x$ from both sides of the equation.

$- x^{2} - 6 x = - 16$

Step 2.2

Add

$16$ to both sides of the equation.

$- x^{2} - 6 x + 16 = 0$

Step 2.3

Factor the left side of the equation.

Tap for more steps...

Step 2.3.1

Factor

$- 1$ out of

$- x^{2} - 6 x + 16$ .

Tap for more steps...

Step 2.3.1.1

Factor

$- 1$ out of

$- x^{2}$ .

$- (x^{2}) - 6 x + 16 = 0$

Step 2.3.1.2

Factor

$- 1$ out of

$- 6 x$ .

$- (x^{2}) - (6 x) + 16 = 0$

Step 2.3.1.3

Rewrite

$16$ as

$- 1 (- 16)$ .

$- (x^{2}) - (6 x) - 1 \cdot - 16 = 0$

Step 2.3.1.4

Factor

$- 1$ out of

$- (x^{2}) - (6 x)$ .

$- (x^{2} + 6 x) - 1 \cdot - 16 = 0$

Step 2.3.1.5

Factor

$- 1$ out of

$- (x^{2} + 6 x) - 1 (- 16)$ .

$- (x^{2} + 6 x - 16) = 0$

$- (x^{2} + 6 x - 16) = 0$

Step 2.3.2

Factor.

Tap for more steps...

Step 2.3.2.1

Factor

$x^{2} + 6 x - 16$ using the AC method.

Tap for more steps...

Step 2.3.2.1.1

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

$- 16$ and whose sum is

$6$ .

$- 2, 8$

Step 2.3.2.1.2

Write the factored form using these integers.

$- ((x - 2) (x + 8)) = 0$

$- ((x - 2) (x + 8)) = 0$

Step 2.3.2.2

Remove unnecessary parentheses.

$- (x - 2) (x + 8) = 0$

$- (x - 2) (x + 8) = 0$

$- (x - 2) (x + 8) = 0$

Step 2.4

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

$0$ , the entire expression will be equal to

$0$ .

$x - 2 = 0$

$x + 8 = 0$

Step 2.5

Set

$x - 2$ equal to

$0$ and solve for

$x$ .

Tap for more steps...

Step 2.5.1

Set

$x - 2$ equal to

$0$ .

$x - 2 = 0$

Step 2.5.2

Add

$2$ to both sides of the equation.

$x = 2$

$x = 2$

Step 2.6

Set

$x + 8$ equal to

$0$ and solve for

$x$ .

Tap for more steps...

Step 2.6.1

Set

$x + 8$ equal to

$0$ .

$x + 8 = 0$

Step 2.6.2

Subtract

$8$ from both sides of the equation.

$x = - 8$

$x = - 8$

Step 2.7

The final solution is all the values that make

$- (x - 2) (x + 8) = 0$ true.

$x = 2, - 8$

$x = 2, - 8$

Enter YOUR Problem

using Amazon.Auth.AccessControlPolicy;

Mathway requires javascript and a modern browser.

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$