using the quadratic formula to solve $x^{2}=5 - x$, what are the values of $x$?\n$\frac{-1pmsqrt{21}}{2}$\n$\…

Explanation:

Step1: Rewrite equation in standard form

First, rewrite $x^{2}=5 - x$ as $x^{2}+x - 5=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 1$, $b = 1$, $c=-5$.

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 1$, $b = 1$, $c=-5$ into it. Calculate $b^{2}-4ac=(1)^{2}-4\times1\times(-5)=1 + 20=21$.

Step3: Find the values of x

Then $x=\frac{-1\pm\sqrt{21}}{2\times1}=\frac{-1\pm\sqrt{21}}{2}$.

Answer:

$\frac{-1\pm\sqrt{21}}{2}$