The equation `2x^(2)+13x+15=0` by
completing the square method

Explanation

by completing the square method :
`2x^(2)+13x+15=4`
`:.x^(2)+(13)/(2)+(15)/(2)=0" "…….` (Dividing by 2)
Comparing `x^(2)+(13)/(2)x" with "x^(2)+2xy`
`2xy=(13)/(2)x" ":.y=(13)/(4)" ":.y^(2)=(169)/(16)`
`x^(2)+(13)/(2)x+(169)/(16)-(169)/(16)+(15)/(2)=0`
`:.(x+(13)/(4))^(2)-((169-120)/(16))=0`
`:.(x+(13)/(4))^(2)-((49)/(16))=0`
`:.(x+(13)/(4))^(2)-((7)/(4))^(2)=0`
`:.(x+(13)/(4)+(7)/(4))(x+(13)/(4)-(7)/(4))=0`
`:.(x+5)(x+(3)/(2))=0`
`:.x+5=0orx+(3)/(2)=0`
`:.x=-5orx=-(3)/(2)`
`(-5,-(3)/(2))` are the roots of the given quadratic equation.