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# 2x 2 - 3 = 6x solve by completing the square

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2x2 - 3 = 6x  solve by completing the square

Guest Mar 8, 2018
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$$2x^2-3=6x\\ \text{Make sure it's in}\,ax^2+bx=c\;\text{form}\\ 2x^2-6x=3\\ \text{Leading coefficient must be 1}\\ x^2-3x=\frac{3}{2}\\ x^2-3x+(\frac{3}{2})^2=\frac{3}{2}+(\frac{3}{2})^2\\ (x-\frac{3}{2})^2=\frac{15}{4}\\ \text{Take the square root of both sides}\\ x-\frac{3}{2}=\pm\frac{\sqrt{15}}{2}\\ x=\frac{3\pm\sqrt{15}}{2}\\ x=\frac{3+\sqrt{15}}{2},\;x=\frac{3\pm\sqrt{15}}{2}$$