Question

Using the quadratic formula to solve x2 = 5 – x, what are the values of x?

Answer 1

Answer:

$\dfrac{-1+\sqrt{21}}{2}$ and $\dfrac{-1-\sqrt{21}}{2}$.

Step-by-step explanation:

The given quadratic equation is

$x^2=5-x$

It is can written as

$x^2+x-5=0$

If a quadratic equation is $ax^2+bx+c=0$, then the quadratic formula is

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

In the given quadratic equation $a=1,b=1,c=-5$. So,

$x=\dfrac{-1\pm \sqrt{1^2-4(1)(-5)}}{2(1)}$

$x=\dfrac{-1\pm \sqrt{1+20}}{2}$

$x=\dfrac{-1\pm \sqrt{21}}{2}$

$x=\dfrac{-1+\sqrt{21}}{2},\dfrac{-1-\sqrt{21}}{2}$

Therefore, the values of x are $\dfrac{-1+\sqrt{21}}{2}$ and $\dfrac{-1-\sqrt{21}}{2}$.