Question

using the quadratic formula to solve ( x^2 = 5 - x ), what are the values of ( x )?
( \frac{-1 pm sqrt{21}}{2} )
( \frac{-1 pm sqrt{19}}{2} )
( \frac{6 pm sqrt{21}}{2} )
( \frac{1 pm sqrt{19}}{2} )

Explanation:

Step1: Rearrange to standard form

$x^2 + x - 5 = 0$

Step2: Identify coefficients

$a=1,\ b=1,\ c=-5$

Step3: Apply quadratic formula

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

Step4: Substitute values

$$x=\frac{-1\pm\sqrt{1^2-4(1)(-5)}}{2(1)}=\frac{-1\pm\sqrt{21}}{2}$$

Answer:

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