Question

Solve using formula.

5x² + 13x + 8 = 0

Answer 1

5x² + 13x + 8 = 0

On comparing with the equation ax² + bx + c = 0

a = 5, b = 13 and c = 8

Now

b² - 4ac = (13)² - 4 × 5 × 8

= 169 - 160

= 9

\[x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}\]

\[x = \frac{- 13 \pm \sqrt{9}}{2 \times 5}\]

\[x = \frac{- 13 \pm 3}{10}\]

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

\[  x = \frac{- 13 + 3}{10} \text{ or } x = \frac{- 13 - 3}{10}\]

\[ x = \frac{- 10}{10} \text{ or } x = \frac{- 16}{10}\]

Rearrange and isolate the variable to find each solution

\[ x = - 1 \text{ or }x = \frac{- 8}{5}\]