Question

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:

If $a{x}^2+bx+c=0$, with $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$50x^2=2$

Short answer

The values of x are $x=\frac{1}{5}$and $x=-\frac{1}{5}$.

Step-by-step solution

- Understand the concept used 

If $a{x}^2+bx+c=0$, with $a\ne 0$, then $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$. Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

- Substitute the values 

It is given that $50x^2=2$which can also be written as $50x^2-2=0$.Using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, substitute 50 for a, 0 for b and -2 for c.

Put the values in the formula and get $x=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(50\right)\times \left(-2\right)}}{2\left(50\right)}$.

- Simplify for x 

Simplify the expression for x.

$\begin{array}{c}x=\frac{0\pm \sqrt{0^2-4\left(50\right)\left(-2\right)}}{2\left(50\right)}\\ =\frac{\pm \sqrt{400}}{100}\\ =\frac{\pm 20}{100}\end{array}$

Therefore, either $x=\frac{20}{100}$ or $x=\frac{-20}{100}$ that is., either $x=\frac{1}{5}$ or $x=-\frac{1}{5}$.