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