Question

What is the factored form of the expression? d^2 = 36d + 324

Answer 1

Answer:

(x-43.45)(x+7.45)=0.

Step-by-step explanation:

We have the quadratic equation $d^{2}=36d+324$ i.e. $d^{2}-36d-324=0$

Now, the roots of the quadratic equation $ax^{2}+bx+c=0$ are given by $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

So, from the given equation, we have,

a = 1, b =-36 , c = -324.

Substituting the values in $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$, we get,

$x=\frac{36\pm \sqrt{(-36)^{2}-4\times 1\times (-324)}}{2\times 1}$

i.e. $x=\frac{36\pm \sqrt{1296+1296}}{2}$

i.e. $x=\frac{36\pm \sqrt{2592}}{2}$

i.e. $x=\frac{36\pm 50.9}{2}$

i.e. $x=\frac{36+50.9}{2}$  and i.e. $x=\frac{36-50.9}{2}$

i.e. $x=\frac{86.9}{2}$  and i.e. $x=\frac{-14.9}{2}$

i.e. x = 43.45 and x = -7.45

Hence, the factored form of the given expression will be (x-43.45)(x+7.45)=0.