Mister Exam
Factor -7*y^2-3*y*x-10*x^2 squared
The solution
You have entered
[src]
2 2 - 7*y - 3*y*x - 10*x
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right)$$
-7*y^2 - 3*y*x - 10*x^2
The perfect square
Let's highlight the perfect square of the square three-member
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right)$$
Let us write down the identical expression
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right) = - \frac{271 y^{2}}{40} + \left(- 10 x^{2} - 3 x y - \frac{9 y^{2}}{40}\right)$$
or
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right) = - \frac{271 y^{2}}{40} - \left(\sqrt{10} x + \frac{3 \sqrt{10} y}{20}\right)^{2}$$
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right)$$
Let us write down the identical expression
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right) = - \frac{271 y^{2}}{40} + \left(- 10 x^{2} - 3 x y - \frac{9 y^{2}}{40}\right)$$
or
$$- 10 x^{2} + \left(- x 3 y - 7 y^{2}\right) = - \frac{271 y^{2}}{40} - \left(\sqrt{10} x + \frac{3 \sqrt{10} y}{20}\right)^{2}$$
General simplification
[src]
2 2 - 10*x - 7*y - 3*x*y
$$- 10 x^{2} - 3 x y - 7 y^{2}$$
-10*x^2 - 7*y^2 - 3*x*y
Factorization
[src]
/ / _____\\ / / _____\\ | y*\-3 + I*\/ 271 /| | y*\3 + I*\/ 271 /| |x - ------------------|*|x + -----------------| \ 20 / \ 20 /
$$\left(x - \frac{y \left(-3 + \sqrt{271} i\right)}{20}\right) \left(x + \frac{y \left(3 + \sqrt{271} i\right)}{20}\right)$$
(x - y*(-3 + i*sqrt(271))/20)*(x + y*(3 + i*sqrt(271))/20)
Common denominator
[src]
2 2 - 10*x - 7*y - 3*x*y
$$- 10 x^{2} - 3 x y - 7 y^{2}$$
-10*x^2 - 7*y^2 - 3*x*y
Combinatorics
[src]
2 2 - 10*x - 7*y - 3*x*y
$$- 10 x^{2} - 3 x y - 7 y^{2}$$
-10*x^2 - 7*y^2 - 3*x*y
Rational denominator
[src]
2 2 - 10*x - 7*y - 3*x*y
$$- 10 x^{2} - 3 x y - 7 y^{2}$$
-10*x^2 - 7*y^2 - 3*x*y
Trigonometric part
[src]
2 2 - 10*x - 7*y - 3*x*y
$$- 10 x^{2} - 3 x y - 7 y^{2}$$
-10*x^2 - 7*y^2 - 3*x*y
Assemble expression
[src]
2 2 - 10*x - 7*y - 3*x*y
$$- 10 x^{2} - 3 x y - 7 y^{2}$$
-10*x^2 - 7*y^2 - 3*x*y
Combining rational expressions
[src]
2 - 10*x + y*(-7*y - 3*x)
$$- 10 x^{2} + y \left(- 3 x - 7 y\right)$$
-10*x^2 + y*(-7*y - 3*x)