Question

Use the table to answer the question. x Substituted Evaluate True Statement? 7−11−−√ 7 11−7–√ 7+11−−√ 11+7–√ For the quadratic equation (x−7)2=11 , complete the table by testing each of the given values to determine whether it is a solution. Identify the two solutions to the quadratic equation. (1 point) The smaller of the two solutions is x= . The larger of the two solutions is x= . Remaining Attempts : 3

Answer 1

cool

Answer 2

To solve the quadratic equation \((x - 7)^2 = 11\), we first take the square root of both sides:

\[
x - 7 = \pm\sqrt{11}
\]

This gives us two equations to solve for \(x\):

1. \(x - 7 = \sqrt{11}\)
2. \(x - 7 = -\sqrt{11}\)

Now, we can solve for \(x\) in each case.

**For the first equation:**

\[
x = 7 + \sqrt{11}
\]

**For the second equation:**

\[
x = 7 - \sqrt{11}
\]

Next, we can evaluate the two solutions:

The smaller solution is:

\[
x = 7 - \sqrt{11}
\]

The larger solution is:

\[
x = 7 + \sqrt{11}
\]

Now, we can also evaluate the approximate values of \(\sqrt{11}\):

\(\sqrt{11} \approx 3.317\)

So, the approximate values of the two solutions are:

1. \(x \approx 7 - 3.317 \approx 3.683\)
2. \(x \approx 7 + 3.317 \approx 10.317\)

Finally, we identify the two solutions:

- The smaller of the two solutions is \(x = 7 - \sqrt{11}\).
- The larger of the two solutions is \(x = 7 + \sqrt{11}\).

Thus, you can fill in:

The smaller of the two solutions is \(x = 7 - \sqrt{11}\).
The larger of the two solutions is \(x = 7 + \sqrt{11}\).