Algebra Examples

Prove that a Root is on the Interval
,
Move all terms not containing to the right side of the equation.
Tap for more steps...
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
The Intermediate Value Theorem states that, if is a real-valued continuous function on the interval , and is a number between and , then there is a contained in the interval such that .
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Calculate .
Tap for more steps...
Simplify each term.
Tap for more steps...
Raise to the power of to get .
Multiply by to get .
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Simplify by adding and subtracting.
Tap for more steps...
Add and to get .
Add and to get .
Subtract from to get .
Calculate .
Tap for more steps...
Simplify each term.
Tap for more steps...
Remove parentheses around .
Raising to any positive power yields .
Multiply by to get .
Remove parentheses around .
Raising to any positive power yields .
Multiply by to get .
Multiply by to get .
Simplify by adding zeros.
Tap for more steps...
Add and to get .
Add and to get .
Subtract from to get .
Since is on the interval , solve the equation for at the root.
Tap for more steps...
Rewrite the equation as .
The roots of this equation could not be found algebraically, so the roots were determined numerically.
The Intermediate Value Theorem states that there is a root on the interval because is a continuous function on .
The roots on the interval are located at .
Enter YOUR Problem

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

Please enter an email address
Please enter a valid email address
The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Mathway Premium

Step-by-step work + explanations
  •    Step-by-step work
  •    Detailed explanations
  •    No advertisements
  •    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month
$--.--/year (--%)

Mathway Premium

Visa and MasterCard security codes are located on the back of card and are typically a separate group of 3 digits to the right of the signature strip.

American Express security codes are 4 digits located on the front of the card and usually towards the right.
This option is required to subscribe.
Go Back

Step-by-step upgrade complete!

Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]