Question

Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?

Answer 1

Answer:

$x=1$ ± $i\sqrt{19}$

Step-by-step explanation:

First off let's state the quadratic formula

Quadratic formula

$\frac{-b+\sqrt{b^2-4ac} }{2a}$

$\frac{-b-\sqrt{b^2-4ac} }{2a}$

For this question our quadratic equation is

$x^2+20=2x$

Now before we can apply the quadratic formula we first have to set the equation equal to zero. We do this my moving everything to one side and setting it equal to zero.

In this case, we simply move the 2x to the other side making it negative and setting the equation equal to zero.

$x^2-2x+20=0$

From here we plug in the values to the quadratic equation.

Now incase you don't know

$a =$ Coefficient of $x^2$ value

$b=$ Coefficient of $x$ value

$c=$ The Constant

Now plug in values

$a=1$

$b=-2$

$c=20$

To get the values of x using the quadratic formula we have the plug in the values, we also have to both subtract and add the $\sqrt{b^2-4ac}$ to $-b$

Plug in values into formula

$\frac{2+\sqrt{(-2)^2-4(1)(20)} }{2(1)}$

$\frac{2+\sqrt{-76} }{2}$

$\frac{2+\sqrt{-1} *\sqrt{76} }{2}$

$\frac{2+i *\sqrt{76} }{2}$

$\frac{2+i *\sqrt{4(19)} }{2}$

$\frac{2+i *\sqrt{2^2(19)} }{2}$

$\frac{2+2i \sqrt{19} }{2}$

$x=1+i\sqrt{19}$

Now repeat the steps except subtract from -b rather than add to it.

Final Answer

$x=1$ ± $i\sqrt{19}$

BTW

± = plus and minus