Mister Exam

# Factor x^2-9*x-5 squared

An expression to simplify:

### The solution

You have entered [src]
 2
x  - 9*x - 5
$$\left(x^{2} - 9 x\right) - 5$$
x^2 - 9*x - 5
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 9 x\right) - 5$$
To do this, let's use the formula
$$a x^{2} + b x + c = a \left(m + x\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -9$$
$$c = -5$$
Then
$$m = - \frac{9}{2}$$
$$n = - \frac{101}{4}$$
So,
$$\left(x - \frac{9}{2}\right)^{2} - \frac{101}{4}$$
General simplification [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x
Factorization [src]
/            _____\ /            _____\
|      9   \/ 101 | |      9   \/ 101 |
|x + - - + -------|*|x + - - - -------|
\      2      2   / \      2      2   /
$$\left(x + \left(- \frac{9}{2} + \frac{\sqrt{101}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{101}}{2} - \frac{9}{2}\right)\right)$$
(x - 9/2 + sqrt(101)/2)*(x - 9/2 - sqrt(101)/2)
Combining rational expressions [src]
-5 + x*(-9 + x)
$$x \left(x - 9\right) - 5$$
-5 + x*(-9 + x)
Trigonometric part [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x
-5.0 + x^2 - 9.0*x
-5.0 + x^2 - 9.0*x
Powers [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x
Common denominator [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x
Assemble expression [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x
Rational denominator [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x
Combinatorics [src]
      2
-5 + x  - 9*x
$$x^{2} - 9 x - 5$$
-5 + x^2 - 9*x