Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)^2/9=7 .

Answer 1

To solve the quadratic equation using square roots, first isolate the squared term:

(x+16)^2/9 = 7

Multiply both sides of the equation by 9:

(x+16)^2 = 63

Take the square root of both sides of the equation to solve for x:

√((x+16)^2) = √63

Simplify both sides:

x+16 = ±√63

Now subtract 16 from both sides:

x = -16 ± √63

Rounding to the nearest hundredth:

x ≈ -16 + 7.94 ≈ -8.06

x ≈ -16 - 7.94 ≈ -23.94

Therefore, the solutions to the quadratic equation are x ≈ -8.06 and x ≈ -23.94.