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

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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:
  $$100\left(\frac{3}{10}x^{2}-\frac{4}{25}x+\frac{1}{4}ight)=100	imes 0$$
- step3: Calculate:
  $$30x^{2}-16x+25=0$$
- step4: Solve using the quadratic formula:
  $$x=\frac{16\pm \sqrt{\left(-16ight)^{2}-4	imes 30	imes 25}}{2	imes 30}$$
- step5: Simplify the expression:
  $$x=\frac{16\pm \sqrt{\left(-16ight)^{2}-4	imes 30	imes 25}}{60}$$
- step6: Simplify the expression:
  $$x=\frac{16\pm \sqrt{-2744}}{60}$$
- step7: Simplify the expression:
  $$x=\frac{16\pm 14\sqrt{14}	imes i}{60}$$
- step8: Separate into possible cases:
  $$\begin{align}&x=\frac{16+14\sqrt{14}	imes i}{60}\&x=\frac{16-14\sqrt{14}	imes i}{60}\end{align}$$
- step9: Simplify the expression:
  $$\begin{align}&x=\frac{4}{15}+\frac{7\sqrt{14}}{30}i\&x=\frac{16-14\sqrt{14}	imes i}{60}\end{align}$$
- 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):
  $$	extrm{No real solution}$$
The equation $$0.3x^{2}-0.16x+0.25=0$$ does not have any real solutions.
The equation $$0.3x^{2}-0.16x+0.25=0$$ has no real solutions.

(b)
Question 2

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(b) Question 2