Mister Exam
Factor x^2-6*x-9 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} - 6 x\right) - 9$$
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
$$a = 1$$
$$b = -6$$
$$c = -9$$
Then
$$m = -3$$
$$n = -18$$
So,
$$\left(x - 3\right)^{2} - 18$$
$$\left(x^{2} - 6 x\right) - 9$$
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
$$a = 1$$
$$b = -6$$
$$c = -9$$
Then
$$m = -3$$
$$n = -18$$
So,
$$\left(x - 3\right)^{2} - 18$$
Factorization
[src]
/ ___\ / ___\ \x + -3 + 3*\/ 2 /*\x + -3 - 3*\/ 2 /
$$\left(x + \left(-3 + 3 \sqrt{2}\right)\right) \left(x + \left(- 3 \sqrt{2} - 3\right)\right)$$
(x - 3 + 3*sqrt(2))*(x - 3 - 3*sqrt(2))