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.

Answer 1

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:

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

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

1. For \(x - 7 = \sqrt{11}\): \[ x = 7 + \sqrt{11} \]

2. For \(x - 7 = -\sqrt{11}\): \[ x = 7 - \sqrt{11} \]

Thus, the two solutions to the quadratic equation \((x - 7)^2 = 11\) are:

\[ x = 7 + \sqrt{11} \quad \text{and} \quad x = 7 - \sqrt{11} \]

Next, we will test given values to determine whether they are solutions. You will need to provide the values you want to check. If you have particular values in mind, please list them, and I can update the table accordingly. If you don't have specific values, I can demonstrate how the testing works with some example values.