# Solve the equation. x^{3}-8=x-2

Solve the equation.
$$\displaystyle{x}^{{{3}}}-{8}={x}-{2}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

cyhuddwyr9
Step 1
Consider the given equation.
$$\displaystyle{x}^{{{3}}}-{8}={x}-{2}$$
Step 2
On solving above equation,
$$\displaystyle{x}^{{{3}}}-{8}-{x}+{2}={0}$$
$$\displaystyle{x}^{{{3}}}-{x}-{6}={0}$$
Step 3
Since, the one factor of this equation is (x – 2), so
$$\displaystyle\Rightarrow{\frac{{{x}^{{{3}}}-{x}-{6}}}{{{x}-{2}}}}$$
$$\displaystyle\Rightarrow{x}^{{{2}}}+{2}{x}+{3}$$
Step 4
Now, solving the above quadratic equation
$$\displaystyle{x}^{{{2}}}+{2}{x}+{3}={0}$$
Step 5
Formula used:
$$\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}$$
Step 6
Therefore,
$$\displaystyle{x}={\frac{{-{2}\pm\sqrt{{{2}^{{{2}}}-{4}\times{1}\times{3}}}}}{{{2}\times{1}}}}$$
$$\displaystyle{x}={\frac{{-{2}\pm\sqrt{{{4}-{12}}}}}{{{2}}}}$$
$$\displaystyle{x}={\frac{{-{2}\pm\sqrt{{-{8}}}}}{{{2}}}}$$
$$\displaystyle{x}={\frac{{-{2}\pm{2}{i}\sqrt{{{2}}}}}{{{2}}}}$$
$$\displaystyle{x}=-{1}\pm{i}\sqrt{{{2}}}$$
Step 7
Answer: The factors of the equation is equal to
$$\displaystyle{2},-{1}+{i}\sqrt{{{2}}},-{1}-{i}\sqrt{{{2}}}$$