Final answer:
Divide by 5 to isolate the square root, then square both sides and subtract 3 to solve for x, which yields x = 8.56.
Step-by-step explanation:
To solve the equation 5 times the square root of x plus 3 equals 17, you first isolate the square root on one side:
5 √(x+3) = 17
Next, divide both sides by 5:
√(x+3) = 17 / 5
√(x+3) = 3.4
Now square both sides to remove the square root:
(x+3) = (3.4)²
(x+3) = 11.56
Finally, subtract 3 from both sides to solve for x:
x = 11.56 - 3
x = 8.56
Thus, the solution to the equation is x = 8.56