Question

How do you factor 5x^2 = 10x

Answer 1

To begin factoring, set the equation equal to zero - subtract 10x from each side:

5x² = 10x
5x² - 10x = 0

Next, see if you can pull out a GCF, --greatest common factor-- from both terms. You can pull out 5x:

5x² - 10x = 0
5x(x - 2) = 0

The most you can factor the expression is 5x(x - 2) = 0.

Answer 2

`5x^2 = 10x`


`5x^2-10x=10x-10x`


`5x^2-10x=0`

Use quadratic formula


`\quad x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`


`\mathrm{For\:}\quad a=5,\:b=-10,\:c=0:\quad x_(1,\:2)=(-\left(-10\right)\pm √(\left(-10\right)^2-4\cdot \:5\cdot \:0))/(2\cdot \:5)`


`x=(-\left(-10\right)+√(\left(-10\right)^2-4\cdot \:5\cdot \:0))/(2\cdot \:5):\quad 2`


`x=(-\left(-10\right)-√(\left(-10\right)^2-4\cdot \:5\cdot \:0))/(2\cdot \:5):\quad 0`


`x=2,\:x=0`