11. Determine the aa, bb, and cc values of the equation. Recall that the general quadratic equation written in standard form is: ax^2+bx+c=0ax2+bx+c=0.
x^2-10x+8=0x2−10x+8=0
color(red)(1)x^21x2 color(orange)(-10)x−10x color(blue)(+8)=0+8=0
a=color(red)1color(white)(XXX)b=color(orange)(-10)color(white)(XXX)c=color(blue)(8)a=1XXXb=−10XXXc=8
22. Substitute the aa, bb, and cc values into the quadratic formula.
x=(-b+-sqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a
x=(-(color(orange)(-10))+-sqrt((color(orange)(-10))^2-4(color(red)1)(color(blue)8)))/(2(color(red)1))x=−(−10)±√(−10)2−4(1)(8)2(1)
33. Solve for xx.
x=(10+-sqrt(100-32))/2x=10±√100−322
x=(10+-sqrt(68))/2x=10±√682
x=(10+-2sqrt(17))/2x=10±2√172
x=(2(5+-sqrt(17)))/(2(1))x=2(5±√17)2(1)
x=(color(red)cancelcolor(black)2(5+-sqrt(17)))/(color(red)cancelcolor(black)2(1))
color(green)(x=5+-sqrt(17))
:., x=5+-sqrt(17).
