Mister Exam
Factor x^2+10*x-10 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{2} + 10 x\right) - 10$$
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
$$a = 1$$
$$b = 10$$
$$c = -10$$
Then
$$m = 5$$
$$n = -35$$
So,
$$\left(x + 5\right)^{2} - 35$$
$$\left(x^{2} + 10 x\right) - 10$$
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
$$a = 1$$
$$b = 10$$
$$c = -10$$
Then
$$m = 5$$
$$n = -35$$
So,
$$\left(x + 5\right)^{2} - 35$$
Factorization
[src]
/ ____\ / ____\ \x + 5 - \/ 35 /*\x + 5 + \/ 35 /
$$\left(x + \left(5 - \sqrt{35}\right)\right) \left(x + \left(5 + \sqrt{35}\right)\right)$$
(x + 5 - sqrt(35))*(x + 5 + sqrt(35))
Combining rational expressions
[src]
-10 + x*(10 + x)
$$x \left(x + 10\right) - 10$$
-10 + x*(10 + x)