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

Did you mean to include a picture...

What equation results from completing the squre

saramerguelo

17.01.2022

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:

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

(x + 5) ^ 2 = 40

0,0(0 оценок)