Chapter 4, Problem 8AR

To determine

To Solve: The quadratic equation $50x^2=200$ using factoring or quadratic formula.

Answer to Problem 8AR

The solution of equation is either $x=2$ or $x=-2$

Explanation of Solution

Given information:

The quadratic equation $50x^2=200$

Concept and Formula Used:

Quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where quadratic equation is $a{x}^2+bx+c=0$

Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

Calculation:

It is given that

  $50x^2=200$

The equation can be written as

  $50x^2-200=0$

Solving equation using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Where $a=50,b=0\&c=-200$

Putting the values in the formula

  $\begin{array}{l}x=\frac{-\left(0\right)\pm \sqrt{{\left(0\right)}^2-4\times \left(50\right)\times \left(-200\right)}}{2\left(50\right)}\\ x=\frac{0\pm \sqrt{4000-0}}{100}\\ x=\frac{\pm \sqrt{4000}}{100}\\ x=\frac{\pm 200}{100}\end{array}$

Therefore either $x=\frac{200}{100}=2$ or $x=\frac{-200}{100}=-2$

Either $x=2$ or $x=-2$

Conclusion:

The solution of equation is either $x=2$ or $x=-2$