Factoring Quadratic Formula dead end

[adicus22]

I have looked at many examples online and in my text book and have tried this different ways but still don't get both functions to equal zero. I already know my answer below is wrong after plugging it in but am at a dead end at this point. Please show me what I'm doing wrong. Thank you.

Solve the following by factoring:

a) x^2 - 6x - 16 = 0

Answer: x = 0,10
Show your work here: x= 0 or x(x-6-16)=0
x=0 or x-6- 16=0
x=0 or x-10=0
x=0 or x-10+10=0+10
x=0 or x=10

 

[mmm4444bot]

… still don't get both functions to equal zero …

I do not understand which two "functions" you are talking about.

Also, there does not appear to be any need for the quadratic formula in this exercise, since the instructions call for factoring, instead.

You factored it as x (x - 6 - 16).

This is not correct.

If we multiply out your factored form, we get the following.

x (x - 6 - 16) = x^2 - 6x - 16x

This equals x^2 - 22x, which is not the original polynomial.

The factored form will look like this:

x^2 - 6x - 16 = (x + a) * (x + b)

Find the values for a and b by reasoning from the following.

a * b = -16

a + b = -6

Once you find these two values, then set each factor equal to zero and solve for x.

In other words, solve each of the following equations after substituting in the values you found for a and b.

x + a = 0

x + b = 0

 

[Denis]

A little "story":
some teacher wrote down (x + 3) and (x - 5)
he then decided to multiply these together: (x + 3) * (x - 5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15
he then asked told his students: hey, I got x^2 - 2x - 15 = 0 for you guys to solve by factoring
SO: the students have to come up with (x + 3)(x - 5) = 0, hence x = -3 or x = 5

AND: that's just like your problem :wink:

 

[adicus22]

Thank you both for your help it is very much appreciated. Have a wonderful evening.