Question

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

$16x^4=625$

Short answer

The solution by algebraically is no real solutions $x=\pm 2.5$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$16x^4=625$

Divide both sides by 16

$\begin{array}{l}\frac{16x^4}{16}=\frac{625}{14}\\ x^4=\frac{625}{14}\end{array}$

Take the fourth root to both sides:

$\begin{array}{l}\sqrt[4]{x^4}=\sqrt[4]{\frac{625}{16}}\\ x=\pm \frac{5}{2}\\ x=\pm 2.5\end{array}$

Step 3. Solve the equation graphically.

$16x^4=625$

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

$\begin{array}{l}{y}_1=16x^4\\ y_2=625\end{array}$

Draw the graph:

As we can see that both lines are intersecting at $\left(-2.5,625\right),\left(2.5,625\right)$.

So, the solution is $x=\pm 2.5$.