We can solve the equation 4x^2 + 26 = 71 by first subtracting 26 from both sides to get:
4x^2 = 71 - 26 = 45
Then, divide both sides by 4 to isolate x^2:
x^2 = 45/4
Finally, take the square root of both sides, remembering to include both the positive and negative square roots, but since we are looking for the positive solution, we only consider the positive square root:
x = ± √(45/4)
x = ± (3/2)√5
The positive solution is x = (3/2)√5, which is approximately 3.354.
Therefore, the positive solution to the equation 4x^2 + 26 = 71 is (3/2)√5.