Question

Solve each equation. Check your solution.

$\mathbf{2}x\left(x-\mathbf{5}\right)=\mathbf{0}$

Short answer

The solution of$2x\left(x-5\right)=0$ is $x=\mathbf{0}\mathbf{,}\mathbf{5}$.

Step-by-step solution

Step 1. Write zero product property.

For any real numbers x and y, if$xy=0$ then$x=0,y=0$ or both x and y equal to zero.

Step 2. Apply zero product property.

Apply zero product property to the given equation, $2x\left(x-5\right)=0$.

$$\begin{gathered} 2x=0\text{or}x-5=0 \\ x=0x=5 \end{gathered}$$

Therefore, the roots are 0 and 5.

Step 3. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 0 for x and 5 for x in the given equation and simplify.

$$\begin{gathered} 2\cdot 0\left(0-5\right)\stackrel{?}{=}0 \\ 0=0✓ \end{gathered}$$

$$\begin{gathered} 2\cdot 5\left(5-5\right)\stackrel{?}{=}0 \\ 10\left(0\right)\stackrel{?}{=}0 \\ 0=0✓ \end{gathered}$$

Therefore, the obtained solution is correct.