Question

1. $2x^2 - 3 = -3$
2. $9x^2 - 1 = 63$
3. $x^2 - 1 = 39$
4. $5x^2 = 90$
5. $4x^2 - 30 = 22$
6. $3x^2 + 4 = 166$

© gina wilson (all things algebra®, llc), 2015-2022

Explanation:

Problem 5: $2x^2 - 3 = -3$

Step1: Isolate $2x^2$

Add 3 to both sides.
$2x^2 - 3 + 3 = -3 + 3$
$2x^2 = 0$

Step2: Solve for $x^2$

Divide by 2 on both sides.
$x^2 = \frac{0}{2} = 0$

Step3: Solve for $x$

Take square root of both sides.
$x = \sqrt{0} = 0$

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Problem 6: $9x^2 - 1 = 63$

Step1: Isolate $9x^2$

Add 1 to both sides.
$9x^2 - 1 + 1 = 63 + 1$
$9x^2 = 64$

Step2: Solve for $x^2$

Divide by 9 on both sides.
$x^2 = \frac{64}{9}$

Step3: Solve for $x$

Take square root of both sides.
$x = \pm\sqrt{\frac{64}{9}} = \pm\frac{8}{3}$

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Problem 7: $x^2 - 1 = 39$

Step1: Isolate $x^2$

Add 1 to both sides.
$x^2 - 1 + 1 = 39 + 1$
$x^2 = 40$

Step2: Solve for $x$

Take square root of both sides.
$x = \pm\sqrt{40} = \pm2\sqrt{10}$

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Problem 8: $5x^2 = 90$

Step1: Solve for $x^2$

Divide by 5 on both sides.
$x^2 = \frac{90}{5} = 18$

Step2: Solve for $x$

Take square root of both sides.
$x = \pm\sqrt{18} = \pm3\sqrt{2}$

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Problem 9: $4x^2 - 30 = 22$

Step1: Isolate $4x^2$

Add 30 to both sides.
$4x^2 - 30 + 30 = 22 + 30$
$4x^2 = 52$

Step2: Solve for $x^2$

Divide by 4 on both sides.
$x^2 = \frac{52}{4} = 13$

Step3: Solve for $x$

Take square root of both sides.
$x = \pm\sqrt{13}$

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Problem 10: $3x^2 + 4 = 166$

Step1: Isolate $3x^2$

Subtract 4 from both sides.
$3x^2 + 4 - 4 = 166 - 4$
$3x^2 = 162$

Step2: Solve for $x^2$

Divide by 3 on both sides.
$x^2 = \frac{162}{3} = 54$

Step3: Solve for $x$

Take square root of both sides.
$x = \pm\sqrt{54} = \pm3\sqrt{6}$

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Answer:

1. $x=0$
2. $x=\pm\frac{8}{3}$
3. $x=\pm2\sqrt{10}$
4. $x=\pm3\sqrt{2}$
5. $x=\pm\sqrt{13}$
6. $x=\pm3\sqrt{6}$