Question

2a2 + 3 = 7a

Answer 1

\[\begin{array}{l} 2 a^2+3=7 a \\ \text{subtract }7 a\text{ from both sides} \\ 2 a^2-7 a+3=0 \\ \text{Solve the quadratic equation by completing the square,}\text{}\text{divide both sides by }2 \\ a^2-\frac{7 a}{2}+\frac{3}{2}=0 \\ \text{Subtract }\frac{3}{2}\text{ from both sides} \\ a^2-\frac{7 a}{2}=-\frac{3}{2} \\ \text{add }\frac{49}{16}\text{ to both sides} \\ a^2-\frac{7 a}{2}+\frac{49}{16}=\frac{25}{16} \\ \text{factor the left hand side} \\ \left(a-\frac{7}{4}\right)^2=\frac{25}{16} \\ \text{take the square root of both sides} \\ \left|a-\frac{7}{4}\right|=\frac{5}{4} \\ \text{eliminate the absolute value} \\ a-\frac{7}{4}=-\frac{5}{4}\text{ or }a-\frac{7}{4}=\frac{5}{4} \\ \text{Add }\frac{7}{4}\text{ to both sides} \\ a=\frac{1}{2}\text{ or }a-\frac{7}{4}=\frac{5}{4} \\ \text{Add }\frac{7}{4}\text{ to both sides} \\ a=\frac{1}{2}\text{ or }a=3 \\\end{array}\]