a The square root of a number gives two solutions — one negative and one positive.
B
b First simplify the equation and then solve for x by performing inverse operations.
C
c The inverse operation to a square root is to square.
D
d Can you take the square root of a negative number?
A
a x=± 5
B
b All real numbers.
C
c x=2
D
d No real solutions.
Practice makes perfect
a To solve the equation, we must first eliminate the coefficient to x^2 by dividing both sides by 6. Then we can take the square root of both sides to isolate x.
We have two solutions, x=- 5 and x=5. To check our solutions we substitute them into the original equation. If the left-hand side and right-hand side are equal, the solutions are correct. Let's test the first solution.
b Before we can solve this equation we have to distribute the factor outside of the parentheses on the right-hand side. Then we can perform inverse operations until m is isolated.
Note that squaring an equation can possibly introduce false roots. Therefore, we must test our solution by substituting it into the original equation and then simplify.
d In this equation we have the square of an expression on the left-hand side and a negative number on the right-hand side. Since the square of something is always positive, the left-hand side can never equal - 3 no matter the value of k.
(k-4)^2 ≠- 3
Therefore, there are no real solutions to this equation.
