Respuesta :
Given:
[tex]2n^2+7=-4n+5[/tex]Required:
We need to find the value of n.
Explanation:
Subtract 5 from both sides of the equation.
[tex]2n^2+7-5=-4n+5-5[/tex][tex]2n^2+2=-4n[/tex]Add 4n to both sides of the equation.
[tex]2n^2+2+4n=-4n+4n[/tex][tex]2n^2+2+4n=0[/tex][tex]2n^2+4n+2=0[/tex]DIvide both sides of the equation by 2.
[tex]\frac{2n^2}{2}+\frac{4n}{2}+\frac{2}{2}=0[/tex][tex]n^2+2n+1=0[/tex][tex]Use\text{ 2n=n+n.}[/tex][tex]n^2+n+n+1=0[/tex]Take out the common multiple.
[tex]n(n+1)+1(n+1)=0[/tex][tex](n+1)(n+1)=0[/tex][tex](n+1)^2=0[/tex][tex]n+1=0[/tex]Subtract 1 from both sides.
[tex]n+1-1=0-1[/tex][tex]n=-1[/tex]Final answer:
[tex]n=-1[/tex]