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:

$\begin{gathered} \frac{2x^2}{2}+\frac{8x}{2}+\frac{368}{2}=0 \\ x^2+4x+184=0 \end{gathered}$

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.