Mister Exam
Factor -x^2-5*x+14 squared
The solution
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- x^{2} - 5 x\right) + 14$$
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
$$a = -1$$
$$b = -5$$
$$c = 14$$
Then
$$m = \frac{5}{2}$$
$$n = \frac{81}{4}$$
So,
$$\frac{81}{4} - \left(x + \frac{5}{2}\right)^{2}$$
$$\left(- x^{2} - 5 x\right) + 14$$
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
$$a = -1$$
$$b = -5$$
$$c = 14$$
Then
$$m = \frac{5}{2}$$
$$n = \frac{81}{4}$$
So,
$$\frac{81}{4} - \left(x + \frac{5}{2}\right)^{2}$$
Combining rational expressions
[src]
14 + x*(-5 - x)
$$x \left(- x - 5\right) + 14$$
14 + x*(-5 - x)