# How do you solve d^ { 2} = 50- 23d?

Mar 14, 2017

See below

#### Explanation:

We have ${d}^{2} = 50 - 23 d$, or ${d}^{2} + 23 d - 50 = 0$.
By factoring the latter, we arrive at $\left(d + 25\right) \left(d - 2\right) = 0$.
Thus, $d = - 25 , 2$.

For more information on how to factor polynomials, click the link below.

http://www.instructables.com/id/How-to-factor/

Mar 14, 2017

$d = 2 \mathmr{and} - 25$

#### Explanation:

This is a quadratic function.
First, you need to make it into a quadratic function which looks like this:

${d}^{2} = 50 - 23 d$

Transpose

${d}^{2} + 23 d - 50 = 0$

$\left\{\begin{matrix}a = 1 \\ b = 23 \\ c = - 50\end{matrix}\right.$

$a c = 1 \cdot - 50 = - 50$

Two factors of $- 50$ that give the result of $b$, $23$ are:

$- 2 \mathmr{and} 25$

So

${d}^{2} - 2 d + 25 d - 50 = 0$

Factorize

$d \left(d - 2\right) + 25 \left(d - 2\right) = 0$

$\left(d - 2\right) \left(d + 25\right) = 0$

$d - 2 = 0$

$d = 0 + 2 = 2$

or

$d + 25 = 0$

$d = 0 - 25 = - 25$

$d = 2 \mathmr{and} - 25$