Question

Which area the solutions of the quadratic equation x2=-5x-3

Answer 1

`x =\frac 12\left( -5 +√(13) \right)\\\\ x =\frac 12\left( -5 -√(13) \right)`

Explanation:

`~~~~~x^2 = -5x -3 \\\\\\\implies x^2 +5x =-3\\ \\\implies x^2 + 2 \cdot \frac 52 \cdot x + \left( \frac 52 \right)^2 = -3 + \left( \frac 52 \right)^2\\\\\\\implies \left(x + \frac 52 \right)^2 = -3 + \frac{25}4\\ \\\\\implies \left(x + \frac 52 \right)^2 = (13)/(4)\\\\\\\implies x+ \frac 52 = \pm\sqrt{ \frac{13}4}\\\\\\\implies x + \frac 52 = \pm(√(13))/(2)\\\\\\\implies x = -\frac 52\pm(√(13))/(2)\\\\\\`

`\implies x =\frac 12\left( -5 \pm √(13) \right)`