Q. 425 - Intermediate Algebra

Question

Use the Zero Product Property in the following exercises, solve.

${(2x-1)}^2=0$

Step-by-Step Solution

Answer

The solution of the expression is $x=\frac{1}{2}$.

Step 1. Given and explanation.

We have ${(2x-1)}^2=0$.

We know that the zero product property states that if $a\times b=0$, then either of the factors, both are equal to zero.

So putting them equal to zero will give us the values.

Step 2. Evaluating the values.

We have ${(2x-1)}^2=0$.

Putting under root both sides to eliminate the square gives us $2x-1=0$.

Putting it equal to zero gives

$$\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}$$

This shows that the value is $\frac{1}{2}$.

Step 3. Check the solution.

We will check the solution by putting the value of the solution in the equation separately. If the equation satisfies, our answer is right. 

So, when $x=\frac{1}{2}$, the equation becomes,

$$\begin{gathered} {\left[2\left(\frac{1}{2}\right)-1\right]}^2=0 \\ {(1-1)}^2=0 \\ 0=0 \end{gathered}$$

Thus our calculations are right.