Q58. - Algebra 2

Question

If $\frac{1}{2}{x}^2-6x+2=0$ then x  equal to which if the following?

$\begin{array}{l}\left(A\right)-1.84 \left(B\right)-0.81\\ \left(C\right)0.34 \left(D\right)2.37\end{array}$

Step-by-Step Solution

Answer

The option $\left(C\right)$ is correct.

Step 1. Write down the given inequality.

The given expression is $\frac{1}{2}{x}^2-6x+2=0$. 

Step 2. Solve the given equation.

Solving the inequality $\frac{1}{2}{x}^2-6x+2=0$ by quadratic formula.

$\begin{array}{c}\frac{1}{2}{x}^2-6x+2=\mathrm{0....}\left(\text{Given}\right)\\ x=\frac{-\left(-6\right)\pm \sqrt{{\left(-6\right)}^2-4\left(\frac{1}{2}\right)\left(2\right)}}{2\left(\frac{1}{2}\right)}\\ x=6-4\sqrt{2}\\ x=0.343\end{array}$

The result $x=0.343$ matches with option (C).

Step 3. Conclusion.

The option $\left(C\right)$ is correct.