For this case we must complete squares:
[tex]x ^ 2 + 10x = 15[/tex]
We add the square of half the coefficient of the term "x",
[tex](\frac {b} {2a}) ^ 2[/tex] on both sides of the equation:
[tex]x^2+10x+(\frac {10} {2 (1)}) ^ 2 = 25 + 15\\x ^ 2 + 10x + 5 ^ 2 = 25 + 15[/tex]
According to the perfect square trinomial we have:
[tex](a + b) ^ 2 = a ^2 + 2ab + b ^ 2[/tex]
Rewriting the expression we have:
[tex]a = x\\b = 5\\(x + 5) ^ 2 = 25 + 15\\(x + 5) ^ 2 = 40[/tex]
ANswer:
[tex](x + 5) ^ 2 = 40[/tex]
