Answer:
[tex](x-43.45)(x+7.45)=0[/tex]
Step-by-step explanation:
We have the quadratic equation [tex]d^{2}=36d+324[/tex] i.e. [tex]d^{2}-36d-324=0[/tex]
As, the roots of the quadratic equation [tex]ax^{2}+bx+c=0[/tex] are given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].
So, from the given equation, we have,
a = 1, b = -36 , c = -324.
Substituting the values in [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex], we get,
[tex]x=\frac{36\pm \sqrt{(-36)^{2}-4\times 1\times (-324)}}{2\times 1}[/tex]
i.e. [tex]x=\frac{36\pm \sqrt{1296+1296}}{2}[/tex]
i.e. [tex]x=\frac{36\pm \sqrt{2592}}{2}[/tex]
i.e. [tex]x=\frac{36\pm 50.9}{2}[/tex]
i.e. [tex]x=\frac{36+50.9}{2}[/tex] and [tex]x=\frac{36-50.9}{2}[/tex]
i.e. [tex]x=\frac{86.9}{2}[/tex] and [tex]x=\frac{-14.9}{2}[/tex]
i.e. x = 43.45 and x = -7.45
Thus, the roots of the equation are 43.45 and -7.45.
Hence, the factored form of the given expression will be [tex](x-43.45)(x+7.45)=0[/tex]
