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 can start by simplifying the equation:

−9 + (x − 3)^2 − 4 = −4

First, we can simplify the expression (x - 3)^2 by expanding it:

(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9

Now, we substitute this simplified expression back into the equation:

−9 + x^2 - 6x + 9 − 4 = −4

Next, we combine like terms:

x^2 - 6x - 4 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -6, and c = -4. Plugging these values into the quadratic formula, we get:

x = (-(-6) ± √((-6)^2 - 4(1)(-4))) / (2(1))

Simplifying further:

x = (6 ± √(36 + 16)) / 2

x = (6 ± √52) / 2

x = (6 ± 2√13) / 2

We can simplify this expression by factoring out a 2 in the numerator:

x = (2(3 ± √13)) / 2

The 2 in the numerator and denominator cancel out:

x = 3 ± √13

Therefore, the solutions to the quadratic equation are:

x = 3 + √13 or x = 3 - √13

So the answer is {3 + √13, 3 - √13}. However, none of the given options match this answer, so none of the provided responses are correct.