How do you solve using the completing the square method #x^2 – 5x + 10 = 0#?

1 Answer
Apr 14, 2017

Answer:

#x=+-sqrt15/2 i+5/2#

Explanation:

To #color(blue)"complete the square"#

add #(1/2" coefficient of the x-term")^2" to " x^2-5x#

To retain the balance of the equation this should be added to both sides.

#rArr" add " (-5/2)^2=25/4#

#rArr(x^2-5xcolor(red)(+25/4))+10=0color(red)(+25/4)#

#rArr(x-5/2)^2=25/4-10#

#rArr(x-5/2)^2=-15/4#

Since the right side is negative, the solutions are complex.

#color(blue)"take the square root of both sides"#

#sqrt((x-5/2)^2)=+-sqrt(-15/4)#

#rArrx-5/2=+-sqrt15/2i#

#rArrx=+-sqrt15/2i+5/2#