Answer
$x={\frac{1-\sqrt{3}}{2}}$
Work Step by Step
Set up the equation:
Let $x$ be the number. Note that $x<0$.
$2x^2 - (1+2x)=0$
$2x^2 - 1 - 2x =0$
$2x^2 -2x-1=0$
$x^2 -x-\frac{1}{2}=0$
$x^2 -x=\frac{1}{2}$
Compute for $x$ by completing the square.
The coefficient of the $x$-term is $-1$; $(\frac{-1}{2})^2=\frac{1}{4}$
Add $\frac{1}{4}$ to both sides to complete the square.
$x^2 -2x+\frac{1}{4}=\frac{1}{2}+\frac{1}{4}$
$x^2 -2x+\frac{1}{4}=\frac{3}{4}$
$(x-\frac{1}{2})^2=\frac{3}{4}$
$x-\frac{1}{2}=±\sqrt{\frac{3}{4}}$
$x=\frac{1}{2}±{\frac{\sqrt3}{2}}$
Since $x<0$, thus, $x={\frac{1-\sqrt{3}}{2}}$.
