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Question
Solve using formula.
5x2 + 13x + 8 = 0
Solution
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
\[ x = - 1 \text{ or }x = \frac{- 8}{5}\]
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