Question

you try: solve each equation

1. $v^2 = 81$
2. $x^2 + 7 = 107$
3. $81r^2 + 1 = 82$
4. $36x^2 + 9 = 153$

Explanation:

Equation 1:

Step1: Take square root of both sides

$v = \pm\sqrt{81}$

Step2: Simplify the square root

$v = \pm9$

Equation 2:

Step1: Isolate $x^2$ term

$x^2 = 107 - 7$
$x^2 = 100$

Step2: Take square root of both sides

$x = \pm\sqrt{100}$
$x = \pm10$

Equation 3:

Step1: Isolate $r^2$ term

$81r^2 = 82 - 1$
$81r^2 = 81$

Step2: Solve for $r^2$

$r^2 = \frac{81}{81}$
$r^2 = 1$

Step3: Take square root of both sides

$r = \pm\sqrt{1}$
$r = \pm1$

Equation 4:

Step1: Isolate $x^2$ term

$36x^2 = 153 - 9$
$36x^2 = 144$

Step2: Solve for $x^2$

$x^2 = \frac{144}{36}$
$x^2 = 4$

Step3: Take square root of both sides

$x = \pm\sqrt{4}$
$x = \pm2$

Answer:

1. $v = 9$ or $v = -9$
2. $x = 10$ or $x = -10$
3. $r = 1$ or $r = -1$
4. $x = 2$ or $x = -2$