Mister Exam
Factor -x^2-x+6 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- x^{2} - x\right) + 6$$
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
$$a = -1$$
$$b = -1$$
$$c = 6$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{25}{4}$$
So,
$$\frac{25}{4} - \left(x + \frac{1}{2}\right)^{2}$$
$$\left(- x^{2} - x\right) + 6$$
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
$$a = -1$$
$$b = -1$$
$$c = 6$$
Then
$$m = \frac{1}{2}$$
$$n = \frac{25}{4}$$
So,
$$\frac{25}{4} - \left(x + \frac{1}{2}\right)^{2}$$