Question

Solve the following quadratic equation using square roots: −9+(x−3)^2/−4=−4 .(1 point) Responses {16,−10} left brace 16 comma negative 10 right brace {28,−22} left brace 28 comma negative 22 right brace {8,−2} left brace 8 comma negative 2 right brace {2,−8}

Answer 1

To solve the quadratic equation, we need to isolate the term with the square root. First, we multiply both sides of the equation by -4 to get rid of the fraction:

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

36 - (x-3)^2 = 16

Next, we add (x-3)^2 to both sides of the equation to isolate the squared term:

36 = (x-3)^2 + 16

Subtracting 16 from both sides gives:

20 = (x-3)^2

Now, we can solve for x by taking the square root of both sides:

sqrt(20) = sqrt((x-3)^2)

+- 2sqrt(5) = x-3

Adding 3 to both sides:

3 +- 2sqrt(5) = x

So the solution to the quadratic equation is {3 + 2sqrt(5), 3 - 2sqrt(5)}.