Question

directions: solve using the square roots method. write all answers in simplest form.

1. $x^2 + 4 = 0$
2. $-3x^2 = 150$
3. $2x^2 + 71 = -163$
4. $18 - x^2 = 39$
5. $-4x^2 - 3 = 481$

Explanation:

Problem 16: \( x^2 + 4 = 0 \)

Step 1: Isolate \( x^2 \)

Subtract 4 from both sides:
\( x^2 = -4 \)

Step 2: Take square roots

The square root of a negative number involves the imaginary unit \( i \), where \( i^2 = -1 \). Thus:
\( x = \pm \sqrt{-4} = \pm 2i \)

Problem 17: \( -3x^2 = 150 \)

Step 1: Isolate \( x^2 \)

Divide both sides by -3:
\( x^2 = \frac{150}{-3} = -50 \)

Step 2: Take square roots

Using \( i^2 = -1 \):
\( x = \pm \sqrt{-50} = \pm \sqrt{50}i = \pm 5\sqrt{2}i \)

Problem 18: \( 2x^2 + 71 = -163 \)

Step 1: Isolate \( 2x^2 \)

Subtract 71 from both sides:
\( 2x^2 = -163 - 71 = -234 \)

Step 2: Isolate \( x^2 \)

Divide by 2:
\( x^2 = \frac{-234}{2} = -117 \)

Step 3: Take square roots

Using \( i^2 = -1 \):
\( x = \pm \sqrt{-117} = \pm \sqrt{117}i = \pm 3\sqrt{13}i \)

Problem 19: \( 18 - x^2 = 39 \)

Answer:

s:

1. \( \boldsymbol{x = \pm 2i} \)
2. \( \boldsymbol{x = \pm 5\sqrt{2}i} \)
3. \( \boldsymbol{x = \pm 3\sqrt{13}i} \)
4. \( \boldsymbol{x = \pm \sqrt{21}i} \)
5. \( \boldsymbol{x = \pm 2\sqrt{29}i} \)