Mister Exam
Factor -9*x^2+15*x-11 squared
The solution
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2 - 9*x + 15*x - 11
$$\left(- 9 x^{2} + 15 x\right) - 11$$
-9*x^2 + 15*x - 11
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(- 9 x^{2} + 15 x\right) - 11$$
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
$$a = -9$$
$$b = 15$$
$$c = -11$$
Then
$$m = - \frac{5}{6}$$
$$n = - \frac{19}{4}$$
So,
$$- 9 \left(x - \frac{5}{6}\right)^{2} - \frac{19}{4}$$
$$\left(- 9 x^{2} + 15 x\right) - 11$$
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
$$a = -9$$
$$b = 15$$
$$c = -11$$
Then
$$m = - \frac{5}{6}$$
$$n = - \frac{19}{4}$$
So,
$$- 9 \left(x - \frac{5}{6}\right)^{2} - \frac{19}{4}$$
Factorization
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/ ____\ / ____\ | 5 I*\/ 19 | | 5 I*\/ 19 | |x + - - + --------|*|x + - - - --------| \ 6 6 / \ 6 6 /
$$\left(x + \left(- \frac{5}{6} - \frac{\sqrt{19} i}{6}\right)\right) \left(x + \left(- \frac{5}{6} + \frac{\sqrt{19} i}{6}\right)\right)$$
(x - 5/6 + i*sqrt(19)/6)*(x - 5/6 - i*sqrt(19)/6)
Combining rational expressions
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-11 + 3*x*(5 - 3*x)
$$3 x \left(5 - 3 x\right) - 11$$
-11 + 3*x*(5 - 3*x)