Question

solve using any method (2 pts each)

1. ( 5x^2 + 80 = 0 )
2. ( 3x^2 - 21x = 0 )

Explanation:

Problem 7: Solve \( 5x^2 + 80 = 0 \)

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

Subtract 80 from both sides: \( 5x^2 = -80 \)
Divide both sides by 5: \( x^2 = \frac{-80}{5} = -16 \)

Step 2: Solve for \( x \)

Take square roots of both sides. Recall \( \sqrt{-1} = i \):
\( x = \pm \sqrt{-16} = \pm 4i \)

Problem 8: Solve \( 3x^2 - 21x = 0 \)

Step 1: Factor out GCF

Greatest Common Factor (GCF) of \( 3x^2 \) and \( -21x \) is \( 3x \):
\( 3x(x - 7) = 0 \)

Step 2: Apply Zero-Product Property

If \( ab = 0 \), then \( a = 0 \) or \( b = 0 \):

• \( 3x = 0 \implies x = 0 \)
• \( x - 7 = 0 \implies x = 7 \)

Answer:

s:

1. \( x = \pm 4i \)
2. \( x = 0 \) or \( x = 7 \)