Answer:
The two possible solutions are x = 7, or x = -2
which agree with answer a) in the list of options
Step-by-step explanation:
Start by moving all terms to one side of the equal sign, and then factoring out the constant term:
[tex]x^2-5x-14=0[/tex]
The constant term "-14" has ossible factors: (-1), (1) (-2), (2), (-7), (7), (-14), (14) and we look for a pair whose combining results in "-5" (the coefficient of the middle term. We find (-7) and (2) the appropriate factors, so we use then to split the middle term and then factor by grouping:
[tex]x^2-5x-14=0\\x^2-7\,x+2\,x-14=0\\x(x-7)+2(x-7)=0\\(x-7)\,(x+2) = 0[/tex]
Then if the product of these two binomial factors is zero, it means that the first binomial is zero, or the second one is zero. That is:
( x - 7 ) = 0 which means x = 7
or
( x + 2 ) = 0 which means x = -2
So the two possible solutions are x = 7, or x = -2
