Complete the square for 5x^2+10x-16.
first one to answer gets brainiest

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)

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

step-by-step explanation: