Question

What number must you add to complete the square? x2 + 8x = 11

Answer 1

Answer:

16

Step-by-step explanation:

The number to add on both sides to complete the square is the square of the numerical coefficient that accompanies the term in "x", divided by 2.

That is in our case: $(\frac{8}{2}) ^2 = 4^2=16$

Therefore:

$x^2+8x+16=11+16\\x^2+8x+16 = 27$

That way the left hand side of the equation becomes the perfect square of the binomial: (x+4).

You can also prove that such is correct by developing the square of the binomial:

$(x+4)^{2} = (x+4)(x+4)= x^2+4x+4x+16= x^2+8x+16$