Question

Solve the following quadratic equation using square roots: (x+6)22=8
.(1 point)
ResponsesSolve the following quadratic equation using square roots: (x−1Use inspection to solve the equation x2=36169
, then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)
Responses

{−613}
left brace negative Start Fraction 6 over 13 End Fraction right brace

{−613,613}
left brace negative Start Fraction 6 over 13 End Fraction comma Start Fraction 6 over 13 End Fraction right brace

{613}
left brace Start Fraction 6 over 13 End Fraction right brace

There are no real solutions.8)2=196
.(1 point)
Responses

​ {−4,−32}
​ left brace negative 4 comma negative 32 right brace

{32,4}
left brace 32 comma 4 right brace

{214,−178}
left brace 214 comma negative 178 right brace

{21,5}

{−2,−10}
left brace negative 2 comma negative 10 right brace

{10,−22}
left brace 10 comma negative 22 right brace

{−1.17,−6.83}
left brace negative 1.17 comma negative 6.83 right brace

​ {−0.34,−11.66}
​ left brace negative 0.34 comma negative 11.66 right brace

Answer 1

Let's solve the quadratic equations one by one.

1. **Equation:** \((x + 6)^2 = 8\)
- Take the square root of both sides:
\[
x + 6 = \pm \sqrt{8}
\]
\(\sqrt{8} = 2\sqrt{2}\), so we get:
\[
x + 6 = 2\sqrt{2} \quad \text{or} \quad x + 6 = -2\sqrt{2}
\]
- Solving these gives:
\[
x = 2\sqrt{2} - 6 \quad \text{or} \quad x = -2\sqrt{2} - 6
\]

2. **Equation:** \(x^2 = 36169\)
- Taking the square root of both sides:
\[
x = \pm \sqrt{36169}
\]
Since \(36169 = 189^2\):
\[
x = 189 \quad \text{or} \quad x = -189
\]
- The solution set is \(\{-189, 189\}\).

3. **Next Equation:** \(8^2 = 196\)
- This appears to be checking for \(8^2\) equaling \(196\), but \(8^2 = 64\). Therefore, the equation is incorrect. Let’s assume that the original intention was \(x^2 = 196\).
- Taking the square root of both sides:
\[
x = \pm \sqrt{196}
\]
Since \(196 = 14^2\):
\[
x = 14 \quad \text{or} \quad x = -14
\]
- The solution set is \(\{14, -14\}\).

### Final Responses:

1. For \((x + 6)^2 = 8\):
- Solutions: \(x = 2\sqrt{2} - 6\) and \(x = -2\sqrt{2} - 6\) (exact roots)

2. For \(x^2 = 36169\):
- Solution set: \(\{-189, 189\}\)

3. For \(x^2 = 196\) (if it was intended):
- Solution set: \(\{14, -14\}\).

If there are any specific options available for the solutions, please refer to or provide those options for selection.