Question

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

Answer 1

Answer:

6,24

Step-by-step 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:

$(x-8) ^ 2 = 87$