Mister Exam
Factor x^2+6*x-10 squared
The solution
Factorization
[src]
/ ____\ / ____\ \x + 3 - \/ 19 /*\x + 3 + \/ 19 /
$$\left(x + \left(3 - \sqrt{19}\right)\right) \left(x + \left(3 + \sqrt{19}\right)\right)$$
(x + 3 - sqrt(19))*(x + 3 + sqrt(19))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 6 x\right) - 10$$
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
$$a = 1$$
$$b = 6$$
$$c = -10$$
Then
$$m = 3$$
$$n = -19$$
So,
$$\left(x + 3\right)^{2} - 19$$
$$\left(x^{2} + 6 x\right) - 10$$
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
$$a = 1$$
$$b = 6$$
$$c = -10$$
Then
$$m = 3$$
$$n = -19$$
So,
$$\left(x + 3\right)^{2} - 19$$