For this case we have the following expression:
[tex]x ^ 2 + 2x = 15[/tex]
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:
[tex]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[/tex]
By definition we have to:
[tex](a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2[/tex]
So:
[tex](x + 1) ^ 2 = 16[/tex]
Answer:
[tex](x + 1) ^ 2 = 16[/tex]
