Questions: Quadratic and Polynomial Functions
Solving a quadratic equation using the square root property: Exact...
Solve x^2=27, where x is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas. If there is no solution, click "No solution."
x=
Transcript text: Quadratic and Polynomial Functions
Solving a quadratic equation using the square root property: Exact...
Solve $x^{2}=27$, where $x$ is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas. If there is no solution, click "No solution."
\[
x=
\]
$\square$
$\square$
Solution
Solution Steps
Step 1: Apply the square root property
To solve the equation x2=27, we take the square root of both sides. This gives:
x=±27
Step 2: Simplify the square root
The square root of 27 can be simplified by factoring out perfect squares:
27=9×3=9×3=33
Step 3: Write the final solutions
Substituting the simplified square root back into the equation, we get:
x=±33