To find the solution set of the equation x² = 80, we start by solving for x. We can rewrite the equation as:
x² = 80
Next, we can take the square root of both sides to find the values of x:
x = ±√80
Now, simplifying √80, we get:
√80 = √(16 * 5) = √16 * √5 = 4√5
This gives us two potential solutions for x:
x = 4√5 and x = -4√5
Putting this together, the solution set is:
{4√5, -4√5}
In decimal form, using the approximate value of √5 (which is about 2.236), we can express the solutions as:
x ≈ 8.944 and x ≈ -8.944
Therefore, the complete solution set can be represented as:
{4√5, -4√5} or {8.944, -8.944}
This means that the values of x satisfying the equation x² = 80 are approximately 8.944 and -8.944.