Question

Solve the quadratic equation: $\frac{x^2}{2}-\frac{3}{4}=7\frac{1}{4}$

Answer 1

The given quadratic equation $(x+8{)}^2-5=31$can be simplified as follows:

$\frac{x^2}{2}-\frac{3}{4}=7\frac{1}{4}\Rightarrow \frac{x^2}{2}-\frac{3}{4}=\frac{29}{4}\Rightarrow \frac{x^2}{2}=\frac{29}{4}+\frac{3}{4}\Rightarrow \frac{x^2}{2}=\frac{32}{4}\Rightarrow \frac{x^2}{2}=8\Rightarrow x^2=8\times 2\Rightarrow x^2=16\Rightarrow x=\sqrt{16}\Rightarrow x=\pm 4$

Hence, $x=\pm 4$.