Question

Solve the following quadratic equation.

\[x^2 - \frac{3x}{10} - \frac{1}{10} = 0\]

Answer 1

\[x^2 - \frac{3x}{10} - \frac{1}{10} = 0\] 

\[\Rightarrow 10 x^2 - 3x - 1 = 0\]

Comparing the above equation with ax² + bx + c = 0

a = 10, b = -3, c = -1

∴ Δ = b² - 4ac

= (-3)² - 4(10) (-1)

= 9 + 40

= 49

Now, x = `(-b±sqrt(b^2-4ac))/(2a)`

\[ \Rightarrow x = \frac{- \left( - 3 \right) \pm \sqrt{\left( - 3 \right)^2 - 4 \times 10 \times \left( - 1 \right)}}{2 \times 10}\]

\[ \Rightarrow x = \frac{3 \pm \sqrt{9 + 40}}{20}\]

\[ \Rightarrow x = \frac{3 \pm \sqrt{49}}{20}\]

\[ \Rightarrow x = \frac{3 \pm 7}{20}\]

\[ \Rightarrow x = \frac{3 + 7}{20}, \frac{3 - 7}{20}\]

\[ \Rightarrow x = \frac{10}{20}, \frac{- 4}{20}\]

\[ \Rightarrow x = \frac{1}{2}, \frac{- 1}{5}\]