Final answer:
The quadratic equation 2r^2 - 3 = -39 is solved by first isolating r^2, then taking the square root of both sides, recognizing that the solution involves imaginary numbers, and finally expressing the solutions as r = 3i√2 and r = -3i√2.
Step-by-step explanation:
To solve the quadratic equation 2r^2 - 3 = -39 by taking the square root, first, we need to isolate the r^2 term. Let's start by adding 3 to both sides of the equation:
2r^2 - 3 + 3 = -39 + 3
2r^2 = -36
Now, divide both sides by 2 to get:
r^2 = -18
Next, we take the square root of both sides. Since the right side of the equation is negative, we know the solutions will be imaginary numbers:
r = ±√-18
r = ±√(-1)√(18)
r = ±√(-1)√(9)√(2)
r = ±√(-1) * 3√(2)
r = ± 3i√2
Therefore, the two solutions are r = 3i√2 and r = -3i√2.