Mister Exam
Factor x^2+5*x+7 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 5 x\right) + 7$$
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
$$a = 1$$
$$b = 5$$
$$c = 7$$
Then
$$m = \frac{5}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x + \frac{5}{2}\right)^{2} + \frac{3}{4}$$
$$\left(x^{2} + 5 x\right) + 7$$
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
$$a = 1$$
$$b = 5$$
$$c = 7$$
Then
$$m = \frac{5}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x + \frac{5}{2}\right)^{2} + \frac{3}{4}$$
Factorization
[src]
/ ___\ / ___\ | 5 I*\/ 3 | | 5 I*\/ 3 | |x + - + -------|*|x + - - -------| \ 2 2 / \ 2 2 /
$$\left(x + \left(\frac{5}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{5}{2} + \frac{\sqrt{3} i}{2}\right)\right)$$
(x + 5/2 + i*sqrt(3)/2)*(x + 5/2 - i*sqrt(3)/2)