Question

Please help me with this problem so my son can better understand I have attached an image of the problem

Answer 1

We have to solve for c:

`(c+9)^2=64`

When we have quadratic expressions, we have to take into account that each number has two possible square roots: one positive and one negative.

We can see it in this example: the square root of 4 can be 2 or -2. This is beacuse both (-2)² and 2² are equal to 4.

Then, taking that into account, we can solve this expression as:

`\begin{gathered} (c+9)^2=64 \\ c+9=\pm\sqrt[]{64} \\ c+9=\pm8 \end{gathered}`

We then calculate the first solution for the negative value -8:

`\begin{gathered} c+9=-8 \\ c=-8-9 \\ c=-17 \end{gathered}`

And the second solution for the positive value 8:

`\begin{gathered} c+9=8 \\ c=8-9 \\ c=-1 \end{gathered}`

Then, the two solutions are c = -17 and c = -1.

We can check them replacing c with the corresponding values we have found:

`\begin{gathered} (-17+9)^2=64 \\ (-8)^2=64 \\ 64=64 \end{gathered}`
`\begin{gathered} (-1+9)^2=64 \\ (8)^2=64 \\ 64=64 \end{gathered}`

Both solutions check the equality, so they are valid solutions.

Answer: -17 and -1.