Question

Solve x2 + 12x + 25Hias17 by completing the square. Select all the possible solutions.-6 + 70-6 + 2.7–6 – 276-606-270-6-77

Answer 1

we are given the following expression:

`x^2+12x+25=17`

First, we will subtract 17 to both sides:

`\begin{gathered} x^2+12x+25-17=17-17 \\ x^2+12x+8=0 \end{gathered}`

We get an expression of the form:

`ax^2+bx+c=0`

To complete the square we will add and subtract the following term:

`(b^2)/(4a)`

Replacing the values:

`(12^2)/(4(1))=36`

Therefore, we will add and subtract 36:

`x^2+12x+36-36+8=0`

Now we associate the first three terms:

`(x^2+12x+36)-36+8=0`

Now we factor in the associated terms:

`(x+6)^2-36+8=0`

Solving the operations:

`(x+6)^2-28=0`

Now we solve for "x", first by adding 28 to both sides:

`(x+6)^2=28`

Now we take square root to both sides:

`(x+6)=\sqrt[]{28}`

Now we subtract 6 to both sides:

`x=-6\pm\sqrt[]{28}`

Now we factor 28 as 7*4: