Mathematics

Question

n^2+7n+15=5
show work please

2 Answer

  • n^2+7n+15=5
    n^2 + 7n + 10 = 0
    (n + 5)(n + 2) = 0
    n + 5 = 0
    n = -5
    n + 2 = 0
    n = -2

    Answer: n = -5 and -2
  • [tex]n^2+7n+15=5[/tex]

    [tex]n^2+7n=-10[/tex]

    [tex]n^2+7n+(\frac{7}{2})^2=-10+(\frac{7}{2})^2[/tex]

    [tex]n^2+7n+\frac{49}{4}=-10+\frac{49}{4}[/tex]

    [tex](n+\frac{7}{2})^2=\frac{9}{4}[/tex]

    [tex]n+\frac{7}{2}=\sqrt{\frac{9}{4}}[/tex]

    [tex]n=-\frac{7}{2}+\sqrt{\frac{9}{4}}[/tex]

    [tex]n=-2[/tex]
    [tex]n=-5[/tex]