Question A.SE.3: Find the values of x that satisfy the equation 2x² + 4x = 1.

To solve the given equation for x, we must first put it in the form

ax² + bx + c = 0

and then use the quadratic formula. If

2x² + 4x = 1

then

2x² + 4x – 1 = 0

Using the quadratic formula, where a = 2, b = 4, and c = -1, we have

\begin{aligned}x &=\frac{-4 \pm \sqrt{4^2-4(2)(-1)}}{2(2)}\\&=\frac{-4 \pm \sqrt{16+8}}{4}=\frac{-4 \pm \sqrt{24}}{4}=\frac{-4 \pm 4.899}{4}\end{aligned}

The two solutions are

x=\frac{0.899}{4}=0.225 \quad\text{and}\quad x=\frac{-8.899}{4}=-2.225

If this was a problem in which x represented a concentration, we would say x = 0.225 (in the appropriate units), since a negative number for concentration has no physical meaning.