Question

1. $10n^2 + 9 = 819$
2. $5x^2 - 7 = 13$
3. $3r^2 + 2 = 194$
4. $9n^2 - 9 = 567$

Explanation:

Problem 7: $10n^2 + 9 = 819$

Step1: Subtract 9 from both sides

$10n^2 = 819 - 9$
$10n^2 = 810$

Step2: Divide by 10 on both sides

$n^2 = \frac{810}{10}$
$n^2 = 81$

Step3: Take square root of both sides

$n = \pm\sqrt{81}$
$n = \pm9$

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Problem 8: $5x^2 - 7 = 13$

Step1: Add 7 to both sides

$5x^2 = 13 + 7$
$5x^2 = 20$

Step2: Divide by 5 on both sides

$x^2 = \frac{20}{5}$
$x^2 = 4$

Step3: Take square root of both sides

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

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Problem 9: $3r^2 + 2 = 194$

Step1: Subtract 2 from both sides

$3r^2 = 194 - 2$
$3r^2 = 192$

Step2: Divide by 3 on both sides

$r^2 = \frac{192}{3}$
$r^2 = 64$

Step3: Take square root of both sides

$r = \pm\sqrt{64}$
$r = \pm8$

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Problem 10: $9n^2 - 9 = 567$

Step1: Add 9 to both sides

$9n^2 = 567 + 9$
$9n^2 = 576$

Step2: Divide by 9 on both sides

$n^2 = \frac{576}{9}$
$n^2 = 64$

Step3: Take square root of both sides

$n = \pm\sqrt{64}$
$n = \pm8$

Answer:

1. $n = 9$ or $n = -9$
2. $x = 2$ or $x = -2$
3. $r = 8$ or $r = -8$
4. $n = 8$ or $n = -8$