Answer: x= -1 + √(21/5)
Step-by-step explanation:
The given equation can be written as 5x^2+10x-16=0
keep the x terms on one side and constant on another side
5x^2+ 10x = 16.
Now, to make a complete square like (x+a)^2 = x^2+2xa+a^2.
Divide the given equation by 5 on both sides,
The equation now becomes x^2+2x = 16/5.
The middle term is 2xa=2x
By solving for term "a" in above equation, a= 1
The entire equation of complete square should be x^2+2x+1, which is equal to (x+1)^2
Here, in the equation given in question, +1 is missing to make a complete square.
In order to add 1 we have to simultaneously minus 1 to keep the values in the equation unchanged.
Thus, x^2+2x+1-1 =16/5.
Again moving the constant -1 to other side, we have
x^2+2x+1 =16/5+1
After simplification,
(x+1)^2= 21/5
Taking square root on both sides,
(x+1)= + √(21/5)
The answer is x= -1 + √(21/5)
