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

Answer

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.

Method 1: Isolating

  1. Add to both sides of the equation:
  2. Divide both sides by 4:
  3. Take the square root of both sides:
  4. Simplify the square root:
The solutions are and .

Method 2: Factoring (Difference of Squares)

The equation is in the form , where (so ) and (so ).
The difference of squares factors as .
  1. Factor the expression:
  2. Set each factor equal to zero and solve for :
    Case 1:
    Case 2:
The solutions are and .

Checking the Solutions

We check both solutions by substituting them back into the original equation .
Check 1:
Check 2:

Final Answer Formatting

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: