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$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$50x^2=200$

Short answer

The values of x are$x=2$ and $x=-2$.

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$50x^2=200$which can also be written as$50x^2-200=0$ . Using quadratic formula$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , substitute 50 for a, 0 for b and -200 for c.

Put the values in the formula and get$x=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(50\right)\times (-200)}}{2\left(50\right)}$.

- Simplify for x 

Simplify the expression for x.

$\begin{array}{c}x=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(50\right)\times (-200)}}{2\left(50\right)}\\ =\frac{0\pm \sqrt{40000-0}}{100}\\ =\frac{\pm \sqrt{40000}}{100}\\ =\frac{\pm 200}{100}\end{array}$

Therefore, either $x=\frac{200}{100}$or$x=\frac{-200}{100}$ that is., either $x=2$or $x=-2$.