Complete the square X^2+2x=15

Question

asked Nov 7, 2020 48.6k views

1 Answer

Blandish · Answer 1 · 2020-11-14T18:44:48+0000

For this case we have the following expression:

x ^ 2 + 2x = 15

We must complete squares. To do this, we divide the linear term by 2 and square, we add this to both sides of the equation:

$x ^ 2 + 2x + (\frac {2} {2}) ^ 2 = 15 + (\frac {2} {2}) ^ 2\\x ^ 2 + 2x + 1 ^ 2 = 15 + 1\\x ^ 2 + 2x + 1 ^ 2 = 16$

By definition we have to:

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

So:

(x + 1) ^ 2 = 16

Answer: