Question

Use completing the square to solve the equation x2+16x=−44 . First determine the number you must add to both sides of the equation. What is the correct answer? 64;−8±25⎯⎯√ 44;−8±45⎯⎯√ 256;−8±25⎯⎯√ 64;8±20⎯⎯⎯⎯√

Answer 1

We will add 64 to both sides.

x=8±√20

Explanation:

Here we are given the equation:

`x^(2)+16x=-44`

Now we take half of the coefficient of x and add it to x.

Coefficient of x is 16, half of 16 is 8.

Also we add square of 8 to both sides.

So new equation becomes:

`x^(2)+16x+64=-44+64`

Completing the square:

`(x+8)^(2)=20`

NOw let us simplify it to get the value of x.

Taking square root on both sides:

`x+8=+/-√(20)`

Bringing 8 to the right side:

x=8±√20