Question

solving quadratics using square roots date:___________ per copy each equation onto a separate sheet of paper, show your work, and staple to your assignment sheet to turn in. due in class today 1) $4n^2 - 9 = 91$ 2) $9x^2 + 2 = 101$ 3) $8a^2 - 5 = 795$ 4) $8m^2 - 4 = 68$ 5) $3r^2 + 9 = 243$ 6) $10x^2 + 2 = 542$

Explanation:

1) $4n^2 - 9 = 91$

Step1: Isolate the squared term

Add 9 to both sides:
$4n^2 = 91 + 9$
$4n^2 = 100$

Step2: Solve for $n^2$

Divide by 4:
$n^2 = \frac{100}{4}$
$n^2 = 25$

Step3: Take square roots

$n = \pm\sqrt{25}$
$n = \pm5$

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2) $9x^2 + 2 = 101$

Step1: Isolate the squared term

Subtract 2 from both sides:
$9x^2 = 101 - 2$
$9x^2 = 99$

Step2: Solve for $x^2$

Divide by 9:
$x^2 = \frac{99}{9}$
$x^2 = 11$

Step3: Take square roots

$x = \pm\sqrt{11}$

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3) $8a^2 - 5 = 795$

Step1: Isolate the squared term

Add 5 to both sides:
$8a^2 = 795 + 5$
$8a^2 = 800$

Step2: Solve for $a^2$

Divide by 8:
$a^2 = \frac{800}{8}$
$a^2 = 100$

Step3: Take square roots

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

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4) $8m^2 - 4 = 68$

Step1: Isolate the squared term

Add 4 to both sides:
$8m^2 = 68 + 4$
$8m^2 = 72$

Step2: Solve for $m^2$

Divide by 8:
$m^2 = \frac{72}{8}$
$m^2 = 9$

Step3: Take square roots

$m = \pm\sqrt{9}$
$m = \pm3$

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5) $3r^2 + 9 = 243$

Step1: Isolate the squared term

Subtract 9 from both sides:
$3r^2 = 243 - 9$
$3r^2 = 234$

Step2: Solve for $r^2$

Divide by 3:
$r^2 = \frac{234}{3}$
$r^2 = 78$

Step3: Take square roots

$r = \pm\sqrt{78}$

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6) $10t^2 + 2 = 542$

Step1: Isolate the squared term

Subtract 2 from both sides:
$10t^2 = 542 - 2$
$10t^2 = 540$

Step2: Solve for $t^2$

Divide by 10:
$t^2 = \frac{540}{10}$
$t^2 = 54$

Step3: Simplify square root

$t = \pm\sqrt{54} = \pm\sqrt{9\times6} = \pm3\sqrt{6}$

Answer:

1. $n = 5$ or $n = -5$
2. $x = \sqrt{11}$ or $x = -\sqrt{11}$
3. $a = 10$ or $a = -10$
4. $m = 3$ or $m = -3$
5. $r = \sqrt{78}$ or $r = -\sqrt{78}$
6. $t = 3\sqrt{6}$ or $t = -3\sqrt{6}$