Question

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

$2x^5-243=0$

Short answer

The solution by algebraically is no real solutions $x=2.61$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$2x^5-243=0$

Add 243 to both sides:

$\begin{array}{l}2x^5-243+243=0+243\\ 2x^5=243\\ x^5=\frac{243}{2}\\ x^5=121.5\end{array}$

Take the fifth root to both sides:

$\begin{array}{l}\sqrt[5]{x^5}=\sqrt[5]{121.5}\\ x=2.61\end{array}$

Step 3. Solve the equation graphically.

$2x^5-243=0$

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

$\begin{array}{l}{y}_1=2x^5-243\\ y_2=0\end{array}$

Draw the graph:

As we can see that both lines are intersecting at $\left(2.61,0\right)$.

So, the solution is $x=2.61$.