Question

2x^2 - 15x - 8 = 0Use zero product property to solve for x

Answer 1

From the question

`2x^2-15x-8=0`

To factor this we say

`\begin{gathered} -8*2x^2=-16x^2 \\ so\text{ look for two items such that their sum gives the middle item} \\ -15x,\text{ and their product gives } \\ -16x^2 \\ These\text{ are } \\ -16x+x \end{gathered}`

Replacing this with the middle item and factoring we have

`\begin{gathered} 2x^2-25x-8=0 \\ 2x^2-16x+x-8=0 \\ 2x(x-8)+1(x-8)=0 \\ (2x+1)(x-8)=0 \end{gathered}`

Now, using the product property to solve for x, we have

`\begin{gathered} (2x+1)(x-8)=0 \\ 2x+1=0 \\ 2x=-1 \\ x=-(1)/(2)\text{ or } \\ x-8=0 \\ x=8 \end{gathered}`

Hence the answer is

`x=-(1)/(2),x=8`