How do you solve 9x^2-30x+25=0

Question

campbell_st · Answer

well its a perfect square quadratic... can you factorise it..?

anonymous · Answer

This is what I have so far
9x^2=4.5x
25 is 52ab = 2(x)(5)=10x
I dont think im doing this right ?

campbell_st · Answer

look at it this way

$$(3x)^2 = 9x^2$$

anonymous · Answer

so how do I solve it with (3x^2)

campbell_st · Answer

please read the information

$$3x \times 3x = 9x^2.... or .....(3x)^2 = 9x^2$$

25 = 5 x 5

middle term is negative so its -5

now look at the middle term -30x      is -30x/2 = 3x * -5...?

anonymous · Answer

I still do not know how to solve this.

campbell_st · Answer

ok... are you happy about 3x * 3x = 9x^2

and 25 = -5 * -5

anonymous · Answer

yes i get that, but now what do you do or is that it?

campbell_st · Answer

ok so the factorised form is 

$$9x^2 - 30x + 25 = (3x - 5)^2$$

so 

$$(3x - 5)^2 = 0$$

you need to solve 

$$3x - 5 = 0$$

for the solution...

campbell_st · Answer

can you do that..?

anonymous · Answer

x=1.67

campbell_st · Answer

correct... 

so the steps..

1. factorise

2. solve the factors = 0

well done

anonymous · Answer

You factor the equation first... the factor is (3x-5) ^2. Forgot how to solve with squared factors, but you have to set it to equal 0