Equations with powers, or quadratic equations, are really fun to solve when you don’t have a first degree term (a number on its own).
You should be comfortable with square roots to be able to find the answer without any aids. You should also have control over change sides/change sign and know how to get rid of a number in front of .
Rule
The equation
has the solutions
If you have a problem where the number inside the square root is negative, the equation has no real solution, because you can’t take the square root of a negative number using normal means.
Think About This
Why do you think we can’t take the square root of a negative number?
The square root is defined as . Any number raised to the power of become a positive number because . This means that , even if .
Example 1
Solve the equation .
Solve the equation .
Example 2
Solve the equation .
Solve the equation .
Example 3
Solve the equation .
Solve the equation .