Question

What number must you add to complete the square x^2-16=23

Answer 1

6,24

Explanation:

6,24^2-16= 22,9376 -> 23

Answer 2

For this case we must complete squares:

`x ^ 2-16x = 23`

We add the square of half the coefficient of the term "x",

`(\frac {b} {2a}) ^ 2` on both sides of the equation:

`x ^ 2-16x + (\frac {-16} {2 (1)}) ^ 2 = 23 + (\frac {-16} {2 (1)}) ^ 2\\x ^ 2-16x + (- 8) ^ 2 = 23 + 64`

According to the perfect square trinomial we have:

`(a + b) ^ 2 = a ^2 + 2ab + b ^ 2`

Rewriting the expression we have:

`a = x\\b = -8\\(x-8) ^ 2 = 23 + 64\\(x-8) ^ 2 = 87`

ANswer:

`(x-8) ^ 2 = 87`