Q. 8.121 - Intermediate Algebra

Question

Solve: $\sqrt{m+9}-m+3=0.$

Step-by-Step Solution

Answer

The solution is, $x=7$.

Step 1 Given equation is,

$\sqrt{m+9}-m+3=0$.

The objective is, we need to find the solution for the given expression.

Also we know that,${\left(a-b\right)}^2=a^2-2ab+b^2$.

Step 2 First isolate the radical,

$\sqrt{m+9}=m-3$

Now square on both sides.

$$\begin{gathered} m+9={\left(m-3\right)}^2 \\ m+9=m^2-2\left(m\right)\left(3\right)+{\left(3\right)}^2 \\ m+9=m^2-6m+9 \end{gathered}$$

Simplify it.

$$\begin{gathered} m^2-6m+9-m-9=0 \\ {m}^2-7m=0 \\ m\left(m-7\right)=0 \\ m=0,7 \end{gathered}$$

Step 3 Let us check the answer

Substitute $x=0$ into the equation $\sqrt{m+9}-m+3=0$.

$$\begin{gathered} \sqrt{0+9}-0+3=0 \\ \sqrt{9}+3=0 \\ 3+3=0 \\ 6\ne 0 \end{gathered}$$

which is not true.

Substitute $x=7$ into the equation $\sqrt{m+9}-m+3=0.$

$$\begin{gathered} \sqrt{7+9}-7+3=0 \\ \sqrt{16}-4=0 \\ 4-4=0 \\ 0=0 \end{gathered}$$

So, the solution is, $x=7$