solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)^2/9 = 7
To solve the quadratic equation using square roots, we can start by isolating the squared term on one side of the equation.
First, multiply both sides of the equation by 9 to clear the fraction:
9 * (x+16)^2/9 = 7 * 9
(x+16)^2 = 63
Next, take the square root of both sides of the equation to eliminate the squared term:
√(x+16)^2 = √63
x+16 = ±√63
Now, let's solve for x:
x = -16 ± √63
Rounding to the nearest hundredth, x is approximately:
x ≈ -16 + √63 ≈ -16 + 7.94 ≈ -8.06
x ≈ -16 - √63 ≈ -16 - 7.94 ≈ -23.94
Therefore, the solutions to the quadratic equation are approximately x ≈ -8.06 and x ≈ -23.94.