Mister Exam

# Factor 2*x^2-3*x+5 squared

An expression to simplify:

### The solution

You have entered [src]
   2
2*x  - 3*x + 5
$$\left(2 x^{2} - 3 x\right) + 5$$
2*x^2 - 3*x + 5
Factorization [src]
/              ____\ /              ____\
|      3   I*\/ 31 | |      3   I*\/ 31 |
|x + - - + --------|*|x + - - - --------|
\      4      4    / \      4      4    /
$$\left(x + \left(- \frac{3}{4} - \frac{\sqrt{31} i}{4}\right)\right) \left(x + \left(- \frac{3}{4} + \frac{\sqrt{31} i}{4}\right)\right)$$
(x - 3/4 + i*sqrt(31)/4)*(x - 3/4 - i*sqrt(31)/4)
General simplification [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(2 x^{2} - 3 x\right) + 5$$
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
$$a = 2$$
$$b = -3$$
$$c = 5$$
Then
$$m = - \frac{3}{4}$$
$$n = \frac{31}{8}$$
So,
$$2 \left(x - \frac{3}{4}\right)^{2} + \frac{31}{8}$$
5.0 + 2.0*x^2 - 3.0*x
5.0 + 2.0*x^2 - 3.0*x
Combining rational expressions [src]
5 + x*(-3 + 2*x)
$$x \left(2 x - 3\right) + 5$$
5 + x*(-3 + 2*x)
Combinatorics [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2
Common denominator [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2
Powers [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2
Assemble expression [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2
Rational denominator [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2
Trigonometric part [src]
             2
5 - 3*x + 2*x 
$$2 x^{2} - 3 x + 5$$
5 - 3*x + 2*x^2