Question

Solve the following quadratic equation using square roots:
-9+ (x-3)^
__________ =-4
-4

Answer 1

To solve the quadratic equation using square roots, we will isolate the square term and square root both sides of the equation.

Starting with the given equation:
-9 + (x-3)^2 / -4 = -4

First, multiply both sides of the equation by -4 to eliminate the fraction:
-4(-9 + (x-3)^2 / -4) = -4(-4)

Expand the equation:
36 - (x-3)^2 = 16

Next, add (x-3)^2 to both sides of the equation to isolate the square term:
36 - (x-3)^2 + (x-3)^2 = 16 + (x-3)^2

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

Subtract 16 from both sides of the equation:
20 = (x-3)^2

To eliminate the square, we take the square root of both sides:
±√(20) = ±√((x-3)^2)

Since we are looking for real solutions to the quadratic equation, we only consider the positive square root:
√20 = x - 3

Simplify the square root:
√4 * √5 = x - 3

Simplify further:
2√5 = x - 3

Finally, isolate x by adding 3 to both sides of the equation:
2√5 + 3 = x

Therefore, the solution to the quadratic equation is:
x = 2√5 + 3.