Question

solve ( x^2 - 400 = 0 ) for all solutions.

a ( x = pm 4sqrt{10} )

b ( x = -20 ) only

c this has no real solutions.

d ( x = +20 ) only

e ( x = +4sqrt{10} ) only

f ( x = -20 ) and ( +20 )

Explanation:

Step1: Isolate \( x^2 \)

Start with the equation \( x^2 - 400 = 0 \). Add 400 to both sides:
\( x^2 = 400 \)

Step2: Take square roots

Take the square root of both sides. Remember, square roots have two solutions (positive and negative):
\( x = \pm\sqrt{400} \)

Step3: Simplify the square root

Simplify \( \sqrt{400} \). Since \( 20 \times 20 = 400 \), we get:
\( x = \pm 20 \)

Answer:

F. \( x = -20 \) and \( +20 \)