Question

match each equation with its solution.
equations

1. $x^2 - 4 = 0$
2. $x^2 - 6x = 0$
3. $(x + 2)^2 = 9$

solutions
a. $x = 0, 6$
b. $x = -5, 1$
c. $x = \pm 2$

Explanation:

Step1: Solve $x^2 - 4 = 0$

Rearrange and take roots:
$x^2 = 4$
$x = \pm\sqrt{4} = \pm2$

Step2: Solve $x^2 - 6x = 0$

Factor out $x$:
$x(x - 6) = 0$
Set each factor to 0: $x=0$ or $x-6=0 \implies x=6$

Step3: Solve $(x+2)^2 = 9$

Take square roots:
$x+2 = \pm\sqrt{9} = \pm3$
Solve for $x$:
$x = -2 + 3 = 1$ or $x = -2 - 3 = -5$

Answer:

1. $\boldsymbol{x^2 - 4 = 0}$ matches with $\boldsymbol{C. x = \pm2}$
2. $\boldsymbol{x^2 - 6x = 0}$ matches with $\boldsymbol{A. x = 0, 6}$
3. $\boldsymbol{(x+2)^2 = 9}$ matches with $\boldsymbol{B. x = -5, 1}$