Solve Quadratic Equation 81 - 4b^2 = 0 by Factoring

Published on March 11, 2026

Algebra

Solve the equation 81 - 4b^2 = 0 by recognizing it as a difference of squares, factoring, and finding the roots for b.

Question

Solve the equation. Check your solutions. Write your solutions from least to greatest, separated by a comma, if necessary. 81−4⁢𝑏2=0

Here is the step-by-step solution to the equation

The equation is:

This is a quadratic equation that can be solved by isolating the variable

and then taking the square root, or by recognizing it as a difference of squares.

The solutions are

and

The equation

is in the form

, where

(so

) and

(so

).
The difference of squares factors as

The solutions are

and

We check both solutions by substituting them back into the original equation

Check 1:

Check 2:

The solutions are

and

. We must write them from least to greatest, separated by a comma. Note that

The solutions from least to greatest are: