Final answer:
To solve the quadratic equation 5(x+9)²+41=46, first isolate the squared term, then take the square root of both sides and solve for x.
Step-by-step explanation:
To solve the quadratic equation 5(x+9)²+41=46, we need to first isolate the squared term. Subtracting 41 from both sides gives us 5(x+9)² = 5. Next, divide both sides by 5 to get (x+9)² = 1. Taking the square root of both sides gives us x+9 = ±1. Finally, subtract 9 from both sides to find the two solutions: x = -10 and x = -8.