Chapter 1, Problem 37REAE

Solution

Solve the equation $x^2+3x-1=0$ by square completion method.

The solution for the equation is $x=-\frac{3}{2}\pm \sqrt{\frac{13}{2}}$ .

Given:

The equation is $x^2+3x-1=0$ .

Calculation:

Simplify the equation $x^2+3x-1=0$ by completing square

  $\begin{array}{c}{x}^2+3x-1=0\mathrm{......}\left(\text{Given}\right)\\ x^2+3x=1\mathrm{......}\left(\text{Re}-\text{arrange}\right)\\ x^2+3x+{\left(\frac{3}{2}\right)}^2=1+{\left(\frac{3}{2}\right)}^2\mathrm{......}\left(\text{Add both sides }{\left(\frac{3}{2}\right)}^2\right)\\ {\left(x+\frac{3}{2}\right)}^2=\frac{13}{2}\\ x+\frac{3}{2}=\pm \sqrt{\frac{13}{2}}\mathrm{......}\left(\text{Take square-root}\right)\\ x=-\frac{3}{2}\pm \sqrt{\frac{13}{2}}\end{array}$

Conclusion:

Hence, the solution for the equation is $x=-\frac{3}{2}\pm \sqrt{\frac{13}{2}}$ .