Question 257202
7-6x-x^2=0


reorder the terms so you get:


-x^2 - 6x + 7 = 0


multiply both sides of the equation by -1 to get:


x^2 + 6x - 7 = 0


factor to get:


(x+7) * (x-1) = 0


you get:


x = -7 or x = 1


plug into your original equation to see if these values are good.


your original equation is:


7-6x-x^2=0


when x = -7 this becomes 7 - 6*(-7) - (-7)^2 = 7 + 42 - 49 = 49 - 49 = 0.


when x = 1, this becomes 7 - 6*1 - 1^2 = 7 - 6 - 1 = 7 - 7 = 0.


both values of x are good.


your answer is:


the solution to the equation of 7 - 6x - x^2 = 0 is x = -7 or x = 1.   both solutions are valid.