Question

Find all real solutions of the equation.

$2x^2+x=1$

Short answer

Real solution of the given equation: $x=1/2,-1$

Step-by-step solution

Step 1. Factorize the given equation.

Here we shall first find the factors of this quadratic equation.

$\begin{array}{l}2x^2+x=1\\ 2x^2+x-1=0\\ 2x^2+2x-x-1=0\\ 2x\left(x+1\right)-1\left(x+1\right)=0\\ \left(2x-1\right)\left(x+1\right)=0\end{array}$

Step 2. Here we may put the factors of the equation equal to zero.

$\begin{array}{l}2x-1=0\\ x+1=0\end{array}$

Step 3. Simplify the equations of factors to determine 2 real solutions.

Put factors equal to 0, and determine real solutions.

$\begin{array}{c}\left(2x-1\right)=0\\ 2x=1\\ x=\frac{1}{2}\\ x+1=0\\ x=-1\end{array}$