# Solve the Equation 2cos^(2)x+cos x-1=0

Solve the Equation
$2{\mathrm{cos}}^{2}x+\mathrm{cos}x-1=0$
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Aldo Harrington
$2{\mathrm{cos}}^{2}x+\mathrm{cos}x-1=0$
$\mathrm{cos}x=t;-1\le t\le 1$
$2{t}^{2}+t-1=0$
D=1+8=9
${x}_{1}=\frac{-1+3}{4}=\frac{1}{2}$
${x}_{2}=\frac{-1-3}{4}=-1$
$\mathrm{cos}x=\frac{1}{2}$
$x=+-\mathrm{arccos}\frac{1}{2}+2\pi \ast n$
$x=+-\frac{\pi }{3}+2\pi \ast n$
$x=+-\frac{\pi }{3}+2\pi \ast n$
$\mathrm{cos}x=-1$
$x=+-\left(\pi -\mathrm{arccos}1\right)+2\pi \ast k$
$x=+-\pi +2\pi \ast k$
n and k $\in$ Z.