Precalculus Examples

$2 x^{2} e^{2 x} + 2 x e^{2 x} = 0$

Step 1

Factor $2 x e^{2 x}$ out of $2 x^{2} e^{2 x} + 2 x e^{2 x}$ .

Tap for more steps...

Step 1.1

Factor $2 x e^{2 x}$ out of $2 x^{2} e^{2 x}$ .

$2 x e^{2 x} (x) + 2 x e^{2 x} = 0$

Step 1.2

Factor $2 x e^{2 x}$ out of $2 x e^{2 x}$ .

$2 x e^{2 x} (x) + 2 x e^{2 x} (1) = 0$

Step 1.3

Factor $2 x e^{2 x}$ out of $2 x e^{2 x} (x) + 2 x e^{2 x} (1)$ .

$2 x e^{2 x} (x + 1) = 0$

Step 2

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

$x = 0$

$e^{2 x} = 0$

$x + 1 = 0$

Step 3

Set $x$ equal to $0$ .

$x = 0$

Step 4

Set $e^{2 x}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $e^{2 x}$ equal to $0$ .

$e^{2 x} = 0$

Step 4.2

Solve $e^{2 x} = 0$ for $x$ .

Tap for more steps...

Step 4.2.1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{2 x}) = \ln (0)$

Step 4.2.2

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 4.2.3

There is no solution for $e^{2 x} = 0$

No solution

Step 5

Set $x + 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 5.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 6

The final solution is all the values that make $2 x e^{2 x} (x + 1) = 0$ true.

$x = 0, - 1$