Question

Put the following equation in the form (x+a)^2=b2x^2 + 9x = x - 368

Answer 1

we are given the following equation:

`2x^2+9x=x-368`

we are asked to put this equation in the form:

`(x+a)^2=b`

first, let's subtract x on both sides:

`\begin{gathered} 2x^2+9x-x=-368 \\ 2x^2+8x=-368 \end{gathered}`

Now we add 368 on both sides:

`2x^2+8x+368=0`

Now we will divide by "2" both sides of the equation:

`\begin{gathered} (2x^2)/(2)+(8x)/(2)+(368)/(2)=0 \\ x^2+4x+184=0 \end{gathered}`

Now we will separate 184 as 180 + 4, like this:

`x^2+4x+180+4=0`

Now we will factor the expression as a perfect square trinomial, like this:

`\begin{gathered} (x^2+4x+4)+180=0 \\ (x+2)^2+180=0 \end{gathered}`

Now we will subtract 180 on both sides:

`(x+2)^2=-180`

And thus we have obtained the desired form for the expression.