Solve the following quadratic equation using square roots: −9+(x−3)2/−4=−4

Answer 1

To solve the quadratic equation using square roots, we will first simplify the equation:

-9 + (x - 3)^2 / -4 = -4

Multiply both sides of the equation by -4 to eliminate the fraction:

4(-9) + (x - 3)^2 = 16

-36 + (x - 3)^2 = 16

Next, move -36 to the right side of the equation:

(x - 3)^2 = 16 + 36

(x - 3)^2 = 52

Now, take the square root of both sides of the equation:

√(x - 3)^2 = ±√52

x - 3 = ±√52

Now, solve for x by adding 3 to both sides of the equation:

x = 3 ± √52

Therefore, the solution to the quadratic equation is:

x = 3 + √52 or x = 3 - √52