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

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asked Jun 8, 2020 71.3k views

2 Answers

Rob Conklin · Answer 1 · 2020-06-13T07:45:52+0000

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:

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

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