Chapter 1 - 1.4 - Quadratic Equations and Applications - 1.4 Exercises - Page 110: 37

Solutions: $x=1+\frac{\sqrt 2}{2}$ $x=1-\frac{\sqrt 2}{2}$

$6x^2-12x=-3$ (divide both sides by 6) $x^2-2x=-\frac{3}{6}$ $x^2-2(1)x+1^2=-\frac{1}{2}+1^2$ $(x-1)^2=\frac{1}{2}$ $x-1=±\sqrt {\frac{1}{2}}=±\frac{1}{\sqrt 2}\frac{\sqrt 2}{\sqrt 2}=±\frac{\sqrt 2}{2}$ $x=1+\frac{\sqrt 2}{2}$ or $x=1-\frac{\sqrt 2}{2}$