# Exercise ID197

Algebra → Quadratic equations, inequalities and systems of equations → Equations Reducible to Quadratic Form
[Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 18] [Number of characters: 0]

Solve the following equation.

$\frac{{x}^{3}+216}{{x}^{3}}=36-{x}^{3}$

$\frac{{x}^{3}+216}{{x}^{3}}=36-{x}^{3}\phantom{\rule{0ex}{0ex}}$ $\frac{{x}^{3}+216}{{{x}}^{3}}·{{x}}^{3}=36·{x}^{3}-{x}^{3}·{x}^{3}\phantom{\rule{0ex}{0ex}}$ ${x}^{3}+216=36{x}^{3}-{x}^{6}\phantom{\rule{0ex}{0ex}}$ ${x}^{6}+{x}^{3}-36{x}^{3}+216=0\phantom{\rule{0ex}{0ex}}$ ${x}^{6}-35{x}^{3}+216=0\phantom{\rule{0ex}{0ex}}$ ${t}^{2}-35t+216=0\phantom{\rule{0ex}{0ex}}$ ${t}_{1,2}=\frac{35±\sqrt{{35}^{2}-4·1·216}}{2·1}\phantom{\rule{0ex}{0ex}}$ ${t}_{1,2}=\frac{35±\sqrt{1225-864}}{2}=\frac{35±\sqrt{361}}{2}=\frac{35±19}{2}\phantom{\rule{0ex}{0ex}}$ ${t}_{1}=\frac{35+19}{2}=\frac{54}{2}=27\phantom{\rule{0ex}{0ex}}$ ${t}_{2}=\frac{35-19}{2}=\frac{16}{2}=8\phantom{\rule{0ex}{0ex}}$
HELP AVAILABLE!
${x}_{1}=3;{x}_{2}=2$

${a}^{n}·{a}^{m}={a}^{n+m}$

${x}_{1,2}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a};a{x}^{2}+bx+c=0$