(b) \( 0.3 x^{2}-0.16 x+0.25=0 \) Question 2

Solve the equation \( 0.3x^2-0.16x+0.25=0 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(0.3x^{2}-0.16x+0.25=0\) - step1: Convert the decimal into a fraction: \(\frac{3}{10}x^{2}-\frac{4}{25}x+\frac{1}{4}=0\) - step2: Multiply both sides: \(100\left(\frac{3}{10}x^{2}-\frac{4}{25}x+\frac{1}{4}\right)=100\times 0\) - step3: Calculate: \(30x^{2}-16x+25=0\) - step4: Solve using the quadratic formula: \(x=\frac{16\pm \sqrt{\left(-16\right)^{2}-4\times 30\times 25}}{2\times 30}\) - step5: Simplify the expression: \(x=\frac{16\pm \sqrt{\left(-16\right)^{2}-4\times 30\times 25}}{60}\) - step6: Simplify the expression: \(x=\frac{16\pm \sqrt{-2744}}{60}\) - step7: Simplify the expression: \(x=\frac{16\pm 14\sqrt{14}\times i}{60}\) - step8: Separate into possible cases: \(\begin{align}&x=\frac{16+14\sqrt{14}\times i}{60}\\&x=\frac{16-14\sqrt{14}\times i}{60}\end{align}\) - step9: Simplify the expression: \(\begin{align}&x=\frac{4}{15}+\frac{7\sqrt{14}}{30}i\\&x=\frac{16-14\sqrt{14}\times i}{60}\end{align}\) - step10: Simplify the expression: \(\begin{align}&x=\frac{4}{15}+\frac{7\sqrt{14}}{30}i\\&x=\frac{4}{15}-\frac{7\sqrt{14}}{30}i\end{align}\) - step11: Rewrite: \(x_{1}=\frac{4}{15}-\frac{7\sqrt{14}}{30}i,x_{2}=\frac{4}{15}+\frac{7\sqrt{14}}{30}i\) - step12: Remove the complex number(s): \(\textrm{No real solution}\) The equation \(0.3x^{2}-0.16x+0.25=0\) does not have any real solutions.