Question

Use the quadratic formula to determine the exact solutions to the equation.

x^2-4x-8=0
x=____ or x=_____

Answer 1

`x^2-4x-8=0\\\\a=1;\ b=-4;\ c=-8\\\\b^2-4ac=(-4)^2-4\cdot1\cdot(-8)=16+32=48\\\\√(b^2-4ac)=√(48)=√(16\cdot3)=√(16)\cdot\sqrt3=4\sqrt3\\\\x_1=(-b-√(b^2-4ac))/(2a);\ x_2=(-b+√(b^2-4ac))/(2a)\\\\x_1=(-(-4)-4\sqrt3)/(2\cdot1)=(4-4\sqrt3)/(2)=2-2\sqrt3\\\\x_2=(-(-4)+4\sqrt3)/(2\cdot1)=(4+4\sqrt3)/(2)=2+2\sqrt3`