Mister Exam

# Factor -9*p^2-5*p-4 squared

An expression to simplify:

### The solution

You have entered [src]
     2
- 9*p  - 5*p - 4
$$\left(- 9 p^{2} - 5 p\right) - 4$$
-9*p^2 - 5*p - 4
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 9 p^{2} - 5 p\right) - 4$$
To do this, let's use the formula
$$a p^{2} + b p + c = a \left(m + p\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = -9$$
$$b = -5$$
$$c = -4$$
Then
$$m = \frac{5}{18}$$
$$n = - \frac{119}{36}$$
So,
$$- 9 \left(p + \frac{5}{18}\right)^{2} - \frac{119}{36}$$
Factorization [src]
/             _____\ /             _____\
|    5    I*\/ 119 | |    5    I*\/ 119 |
|p + -- + ---------|*|p + -- - ---------|
\    18       18   / \    18       18   /
$$\left(p + \left(\frac{5}{18} - \frac{\sqrt{119} i}{18}\right)\right) \left(p + \left(\frac{5}{18} + \frac{\sqrt{119} i}{18}\right)\right)$$
(p + 5/18 + i*sqrt(119)/18)*(p + 5/18 - i*sqrt(119)/18)
General simplification [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
Common denominator [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
Trigonometric part [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
Combining rational expressions [src]
-4 + p*(-5 - 9*p)
$$p \left(- 9 p - 5\right) - 4$$
-4 + p*(-5 - 9*p)
-4.0 - 5.0*p - 9.0*p^2
-4.0 - 5.0*p - 9.0*p^2
Powers [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
Combinatorics [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
Assemble expression [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
Rational denominator [src]
        2
-4 - 9*p  - 5*p
$$- 9 p^{2} - 5 p - 4$$
-4 - 9*p^2 - 5*p
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