Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

Find the real solutions, if any, of the equation $2x^2+x-1=0$.

Step-by-Step Solution

Answer

The real solutions of the equation are $x=-1,\frac{1}{2}$.

Step 1. Given Information

The given equation is $2x^2+x-1=0$.

We need to find the real solutions of the equation.

Step 2. Simplifying the equation

The equation can also be written as:

$$\begin{gathered} 2x^2+2x-x-1=0 \\ \Rightarrow 2x(x+1)-(x+1)=0 \\ \Rightarrow (2x-1)(x+1)=0 \end{gathered}$$

Step 3. Finding the solutions

When $$\begin{gathered} (2x-1)=0 \\ \Rightarrow 2x=1 \\ \Rightarrow x=\frac{1}{2} \end{gathered}$$

and when $$\begin{gathered} (x+1)=0 \\ \Rightarrow x=-1 \end{gathered}$$