Question

What equation results from completing the squre and then factoring x^2+10=15

Answer 1

For this case we must complete squares:

`x ^ 2 + 10x = 15`

We add the square of half the coefficient of the term "x",

`(\frac {b} {2a}) ^ 2` on both sides of the equation:

`x^2+10x+(\frac {10} {2 (1)}) ^ 2 = 25 + 15\\x ^ 2 + 10x + 5 ^ 2 = 25 + 15`

According to the perfect square trinomial we have:

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

Rewriting the expression we have:

`a = x\\b = 5\\(x + 5) ^ 2 = 25 + 15\\(x + 5) ^ 2 = 40`

ANswer:

`(x + 5) ^ 2 = 40`