Mathematics: What equation results from completing the square and then factoring? x^2+2x=9 a. (x+2)^2=8 b. (x+1)^2=8 c.(x+1)^2=10 d.(x+2)^2=10

932Step-by-step explanation:...

What equation results from completing the square

nothingworksoutforme

28.01.2022

c.(x+1)^2=10

Step-by-step explanation:

Completing the square:

We use the following relation:

$(x + a)^{2} = x^{2} + 2ax + a^{2}$

In this question:

$(x + a)^{2} = x^{2} + 2ax + a^{2} = x^{2} + 2x + a^{2}$

We have to find a.

2a = 2

$a = \frac{2}{2}$

a = 1

$x^{2} + 2x + 1 = (x+1)^{2}$

Thus, we have to add 1 on the right side of the equality.

We end up with:

$(x+1)^{2} = 9 + 1$

$(x+1)^{2} = 10$

So the correct answer is:

c.(x+1)^2=10

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