Question

1. $2x^2 + 71 = -163$
2. $-4x^2 - 3 = 481$

Explanation:

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

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

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

Step 2: Solve for \(x^2\)

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

Since the square of a real number cannot be negative, there are no real solutions. For complex solutions, we can write:
\(x = \pm \sqrt{-117} = \pm 3\sqrt{13}i\)

Problem 19: \(-4x^2 - 3 = 481\)

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

Add 3 to both sides:
\(-4x^2 = 481 + 3\)
\(-4x^2 = 484\)

Step 2: Solve for \(x^2\)

Divide both sides by \(-4\):
\(x^2 = \frac{484}{-4}\)
\(x^2 = -121\)

Since the square of a real number cannot be negative, there are no real solutions. For complex solutions, we can write:
\(x = \pm \sqrt{-121} = \pm 11i\)

Answer:

s:

1. No real solutions; Complex solutions: \(x = \pm 3\sqrt{13}i\)
2. No real solutions; Complex solutions: \(x = \pm 11i\)