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

[AI-generated answer — Explain Bot]

To solve the quadratic equation using square roots, start by isolating the squared term:

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

Combine like terms:

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

(x - 3)^2 = 9

To eliminate the square, take the square root of both sides of the equation:

√((x - 3)^2) = √9

(x - 3) = ±3

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

x - 3 + 3 = ±3 + 3

x = 3 ± 3

This leads to two possible solutions:

x = 3 + 3 = 6
x = 3 - 3 = 0

Therefore, the solutions to the quadratic equation −9 + (x - 3)^2 - 4 = -4 are {6, 0}.

Answer 2

[AI-generated answer — Bot GPT 3.5]

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.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To solve the quadratic equation \(−9+(x−3)^2−4=−4\), we can start by simplifying the equation:

\[−9+(x−3)^2−4=−4\]

Combine like terms:

\[−9+(x−3)^2=0\]

Add 9 to both sides:

\[(x−3)^2=9\]

Next, we can take the square root of both sides:

\[√(x−3)^2=√9\]

Simplify:

\[x−3=±3\]

Adding 3 to both sides:

\[x=3±3\]

The two solutions are:

\[x=6 \text{ or } x=0\]

Therefore, the correct answer is:

{6, 0}