Question

quadratic and polynomial functions
solving an equation of the form ( x^2 = a ) using the square root property
solve ( w^2 = -64 ), where ( w ) is a real number.
simplify your answer as much as possible.
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
( w = )

Explanation:

Step1: Recall square of real number

The square of any real number \( w \) (i.e., \( w^2 \)) is always non - negative. Mathematically, for any real number \( w \), \( w^2\geq0 \).

Step2: Analyze the given equation

We are given the equation \( w^2=- 64 \). But we know that the left - hand side \( w^2 \) (for real \( w \)) is greater than or equal to 0, and the right - hand side is - 64 which is less than 0. Since a non - negative number cannot be equal to a negative number, there is no real number \( w \) that satisfies the equation \( w^2=-64 \).

Answer:

No solution