1. [tex]x^{2} -10x +25 = 0[/tex]
These two numbers are: -5 and -5
-5 + (-5) = -10
-5 * -5 = 25
so...
(x - 5)(x - 5)
To find the roots set the factored numbers equal to zero and solve for x:
x - 5 = 0
x = 5
2. [tex]x^{2} + 9x = -14[/tex]
This equation needs to be equal to zero, so bring -14 to the other side by adding 14 to both sides
[tex]x^{2}+9x+14 =0[/tex]
Find two numbers that the sum is equal to 9 AND the multiplication of the numbers is 14
These numbers are 7 and 2
7 + 2 = 9
7*2 = 14
so...
(x + 2) (x + 7)
To find the roots set the each of the factored numbers equal to zero and solve for x:
x + 2 = 0
x = -2
x + 7 = 0
x = -7
3. [tex]3x^{2} = 6x[/tex]
This equation needs to be equal to zero, so bring 6x to the other side by subtracting 6x to both sides
[tex]3x^{2} -6x = 0[/tex]
In this equation you can factor out a 3 and an x:
3x (x - 2)
To find the roots set the each of the factored numbers equal to zero and solve for x:
3x = 0
3x/3 = 0/3
x = 0
x - 2 = 0
x = 2
Hope this helped!
