# How do you solve  5x^2 - 12x + 10 = x^2 + 10x?

Mar 11, 2016

4 and 5

#### Explanation:

$y = 5 {x}^{2} - 12 x + 10 - {x}^{2} - 10 x = 0$
$y = 4 {x}^{2} - 22 x + 10 = 0.$
Use the new Transforming Method (Google, Yahoo).
Transformed equation: $y ' = {x}^{2} - 22 x + 40 = 0$
Factor pairs of (ac = 40) --> (2, 20). This sum is 22 = -b.
Therefor, the 2 real roots of y' are: y1 = 2 and y2 = 20.
Back to original equation y, the 2 real roots are:
$x 1 = \frac{y 1}{a} = \frac{2}{4} = \frac{1}{2}$ and $x 2 = \frac{y 2}{a} = \frac{20}{4} = 5$
Answers: $\frac{1}{2}$ and 5.
NOTE.
There is no need to factor by grouping and solving the 2 binomials.