Precalculus Examples

Solve for x e^x-30e^(-x)-1=0
Step 1
Rewrite as exponentiation.
Step 2
Substitute for .
Step 3
Simplify each term.
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Step 3.1
Rewrite the expression using the negative exponent rule .
Step 3.2
Combine and .
Step 3.3
Move the negative in front of the fraction.
Step 4
Solve for .
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Step 4.1
Find the LCD of the terms in the equation.
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Step 4.1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 4.1.2
The LCM of one and any expression is the expression.
Step 4.2
Multiply each term in by to eliminate the fractions.
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Step 4.2.1
Multiply each term in by .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Simplify each term.
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Step 4.2.2.1.1
Multiply by .
Step 4.2.2.1.2
Cancel the common factor of .
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Step 4.2.2.1.2.1
Move the leading negative in into the numerator.
Step 4.2.2.1.2.2
Cancel the common factor.
Step 4.2.2.1.2.3
Rewrite the expression.
Step 4.2.3
Simplify the right side.
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Step 4.2.3.1
Multiply by .
Step 4.3
Solve the equation.
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Step 4.3.1
Factor using the AC method.
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Step 4.3.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 4.3.1.2
Write the factored form using these integers.
Step 4.3.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.3.3
Set equal to and solve for .
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Step 4.3.3.1
Set equal to .
Step 4.3.3.2
Add to both sides of the equation.
Step 4.3.4
Set equal to and solve for .
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Step 4.3.4.1
Set equal to .
Step 4.3.4.2
Subtract from both sides of the equation.
Step 4.3.5
The final solution is all the values that make true.
Step 5
Substitute for in .
Step 6
Solve .
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Step 6.1
Rewrite the equation as .
Step 6.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 6.3
Expand the left side.
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Step 6.3.1
Expand by moving outside the logarithm.
Step 6.3.2
The natural logarithm of is .
Step 6.3.3
Multiply by .
Step 7
Substitute for in .
Step 8
Solve .
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Step 8.1
Rewrite the equation as .
Step 8.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 8.3
The equation cannot be solved because is undefined.
Undefined
Step 8.4
There is no solution for
No solution
No solution
Step 9
List the solutions that makes the equation true.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: