20-9x+x^2=0 Solve equation by factoring?

Here’s the answer.

20-9x+x^2=0 –> Write the problem.

x^2-9x+20=0 –> Switch the terms of the above equation around. The x^2 term should go first, then the x term and finally the constant term.

x^2-5x-4x+20=0 –> Change -9x as the sum of -5x and -4x.

x(x-5)-4(x-5)=0 –> Factor out the x in x^2-5x and factor out the -4 in -4x+20.

(x-5)(x-4)=0 –> Write the answer in factored form.

x-5=0 or x-4=0 –> Use zero-product property i.e. if pq=0, then p=0 or q=0.

x=5 or x=4 –> Solve for x.

{4,5} Write the solutions in a set.

So the answer is x=4 or x=5, or {4,5}.

Hope it helps!

2. find two numbers that mulitply to +20 and add to make -9

3. -4, -5

4. 0= (x-4)(x-5)

5. x-4= 0 then x = 4

6. x- 5 = 0 then x = 5

7. x is either 4 or 5

This “Master product rule” doesn’t seem to be taught as often as it once was, use it and you’ll always be set.

x^2 – 9x + 20 = 0

to factor, you need look for two numbers that multiply to 20 and add to -9

the two numbers are -4 and -5

since the leading coefficient is 1, plug the two numbers in factor form

(x – 4) (x – 5) = 0

set each quanity equal to 0

x – 4 = 0

x = 4

x – 5 = 0

x = 5

so x = 4 or 5

hope this helps

That’s just the format I always learned.

x=5

x=4

-5-4= -9

(-5)(-4)=20