Precalculus Examples

Find the Roots (Zeros) x^2e^x-64e^x
Step 1
Set equal to .
Step 2
Solve for .
Tap for more steps...
Step 2.1
Factor the left side of the equation.
Tap for more steps...
Step 2.1.1
Factor out of .
Tap for more steps...
Step 2.1.1.1
Factor out of .
Step 2.1.1.2
Factor out of .
Step 2.1.1.3
Factor out of .
Step 2.1.2
Rewrite as .
Step 2.1.3
Factor.
Tap for more steps...
Step 2.1.3.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.1.3.2
Remove unnecessary parentheses.
Step 2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.3
Set equal to and solve for .
Tap for more steps...
Step 2.3.1
Set equal to .
Step 2.3.2
Solve for .
Tap for more steps...
Step 2.3.2.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.3.2.2
The equation cannot be solved because is undefined.
Undefined
Step 2.3.2.3
There is no solution for
No solution
No solution
No solution
Step 2.4
Set equal to and solve for .
Tap for more steps...
Step 2.4.1
Set equal to .
Step 2.4.2
Subtract from both sides of the equation.
Step 2.5
Set equal to and solve for .
Tap for more steps...
Step 2.5.1
Set equal to .
Step 2.5.2
Add to both sides of the equation.
Step 2.6
The final solution is all the values that make true.
Step 3