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5x^2+8x-69=0 solve by factoring

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1 Answer

Factoring the equation:
 
5 is a prime number, the middle term is positive and the final term is negative, and it's a second degree equation, so we know we have 2 terms, with opposite signs and a 5 and 1 as the x coefficients:
 
(5x+  )(x-   )
 
next we must find the factors of 69.  1&69 don't work because they don't subtract to get 8.   However 3 and 23 work because:
 
23-5(3)=8.  This also tells us that we must end up with a -15 during the FOIL.  So we know that the signs of the constants must be changed and gives us the factors:
 
(5x+23)(x-3)=0
 
To solve for the values of x that make this equation true we set each term equal to 0 and solve them separately.
 
5x+23=0    and x-3 = 0
 
The second is simply a matter of adding 3 to both sides and we get x=3.
The first is 2 operations, subtract 23 from both sides and divide both by 5 and we get x=-23/5
 
So the solutions are x=3, x=-23/5