# How do you solve 9x^2 = x^3 ?

May 18, 2016

$x = 0$
$x = 9$

#### Explanation:

Given -

$9 {x}^{2} = {x}^{3}$
$9 {x}^{2} - {x}^{3} = 0$
${x}^{2} \left(9 - x\right) = 0$
${x}^{2} = 0$
$x = 0$
$9 - x = 0$
$x = 9$

May 19, 2016

# $\implies x = 0 \mathmr{and} 9$

#### Explanation:

While most people would straightaway cancel the ${x}^{2}$ on both sides .I would find that rather foolish.

This is an important concept to have not to cancel x terms on either side of the equation but to bring everything over to one side

$9 {x}^{2} = {x}^{3}$

$9 {x}^{2} - {x}^{3} = 0$

${x}^{2} \left(9 - x\right) = 0$

$\implies {x}^{2} = 0 \mathmr{and} 9 - x = 0$

$\implies x = \pm 0 \mathmr{and} x = 9$

So we get our 3 solutions out of which 2 are not distinct roots