Question 251465
your original equation is:


w^2+3w-10=0


looks like it should factor to be:


(w+5) * (w-2) = 0


multiply (w+5) * (w-2) and you get:


w^2 - 2w + 5w - 10


combine like terms to get:


w^2 + 3w - 10 which is the same as your original equation, confirming that the factors are good.


your equation becomes:


(w+5)*(w-2) = 0


this means that:


either w+5 = 0 or w-2 = 0 or both.


this means that:


w = -5 or w = 2


substitute in your original equation to confirm.


your original equation is:


w^2+3w-10=0


when w = -5, this equation becomes 25 - 15 - 10 = 0


when w = 2, this equation becomes 4 + 6 - 10 = 0


both equations are true confirming the values for x are both good.


your answer is:


the roots of this equation are:


w = -5 and w = 2


a graph of your original equation is shown below confirming graphically that these roots are accurate.


{{{graph(600,600,-10,10,-20,20,x^2+3x-10)}}}