Question

Solve the equation both algebraically and graphically. (Lesson 1.11)

$x^2-32=0$

Short answer

The solution by algebraically is $x\approx 5.7$and graphically is given below:

Step-by-step solution

Step 1. Definition of the intersection point.

An intersection is a single point where two lines meet or cross each other.

Step 2. Solve equation algebraically.

We have$x^2-32=0$

Add 32 both sides:

$\begin{array}{l}{x}^2-32+32=0+32\\ x^2=32\end{array}$

For$x^2=f\left(a\right)$ the solutions are$x=\sqrt{f\left(a\right)},-\sqrt{f\left(a\right)}$

$\begin{array}{l}x=\sqrt{32},-\sqrt{32}\\ x=5.657,-5.657\\ x=5.7,-5.7\end{array}$

Step 3. Solve the equation graphically.

$x^2-32=0$

Now, equate the left side of the equation to $y_1$and the right side to $y_2$.

$\begin{array}{l}{y}_1=x^2-32\\ y_2=0\end{array}$

Draw the graph:

As we can see that both lines are intersecting on $\left(0.567,0\right),\left(-0.567,0\right)$.

So, the solution is $x=\pm 5.7$.