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

1 Answer

4 votes

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

User Tobliug
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