5x^{2}+8x-69=0 Solve by factoring?
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