Question

Solve each problem by using the quadratic formula. Write solutions in simplest radical form. 2x2 + 2x – 2 = 0

Answer 1

$2x^2+2x-2=0 \ \ \ \ \ |\div 2 \\ x^2+x-1=0 \\ \\ a=1 \\ b=1 \\ c=-1 \\ b^2-4ac=1^2-4 \times 1 \times (-1)=1+4=5 \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-1 \pm \sqrt{5}}{2 \times 1}=-\frac{1 \pm \sqrt{5}}{2} \\ \boxed{x=-\frac{1+\sqrt{5}}{2} \hbox{ or } x=-\frac{1-\sqrt{5}}{2}}$