Question

question 31 of 40
solve the equation by using the square root property. write imaginary solutions in
express numbers in simplest form using integers, fractions, or radicals.
$-y^2 + 8 = 12$

Explanation:

Step1: Isolate the \(y^2\) term

Subtract 8 from both sides of the equation \(-y^{2}+8 = 12\):
\(-y^{2}=12 - 8\)
\(-y^{2}=4\)
Multiply both sides by - 1:
\(y^{2}=- 4\)

Step2: Apply the square root property

The square root property states that if \(x^{2}=a\), then \(x=\pm\sqrt{a}\). Here, \(x = y\) and \(a=-4\).
Since \(\sqrt{-4}=\sqrt{4}\times\sqrt{-1}=2i\) (where \(i\) is the imaginary unit with \(i^{2}=-1\)):
\(y=\pm\sqrt{-4}=\pm2i\)

Answer:

\(y = 2i\) or \(y=-2i\)