Solve (3m)^(2)=(2m)^(2)-9 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Solve for m

$m=-\frac{3\sqrt{5}i}{5}\approx -0-1.341640786i$
$m=\frac{3\sqrt{5}i}{5}\approx 1.341640786i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Expand $\left(3m\right)^{2}$.

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

Calculate $3$ to the power of $2$ and get $9$.

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

Expand $\left(2m\right)^{2}$.

$$9m^{2}=2^{2}m^{2}-9$$

Calculate $2$ to the power of $2$ and get $4$.

$$9m^{2}=4m^{2}-9$$

Subtract $4m^{2}$ from both sides.

$$9m^{2}-4m^{2}=-9$$

Combine $9m^{2}$ and $-4m^{2}$ to get $5m^{2}$.

$$5m^{2}=-9$$

Divide both sides by $5$.

$$m^{2}=-\frac{9}{5}$$

The equation is now solved.

$$m=\frac{3\sqrt{5}i}{5}$$ $$m=-\frac{3\sqrt{5}i}{5}$$

Steps Using the Quadratic Formula

Expand $\left(3m\right)^{2}$.

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

Calculate $3$ to the power of $2$ and get $9$.

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

Expand $\left(2m\right)^{2}$.

$$9m^{2}=2^{2}m^{2}-9$$

Calculate $2$ to the power of $2$ and get $4$.

$$9m^{2}=4m^{2}-9$$

Subtract $4m^{2}$ from both sides.

$$9m^{2}-4m^{2}=-9$$

Combine $9m^{2}$ and $-4m^{2}$ to get $5m^{2}$.

$$5m^{2}=-9$$

Add $9$ to both sides.

$$5m^{2}+9=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $5$ for $a$, $0$ for $b$, and $9$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$m=\frac{0±\sqrt{0^{2}-4\times 5\times 9}}{2\times 5}$$

Square $0$.

$$m=\frac{0±\sqrt{-4\times 5\times 9}}{2\times 5}$$

Multiply $-4$ times $5$.

$$m=\frac{0±\sqrt{-20\times 9}}{2\times 5}$$

Multiply $-20$ times $9$.

$$m=\frac{0±\sqrt{-180}}{2\times 5}$$

Take the square root of $-180$.

$$m=\frac{0±6\sqrt{5}i}{2\times 5}$$

Multiply $2$ times $5$.

$$m=\frac{0±6\sqrt{5}i}{10}$$

Now solve the equation $m=\frac{0±6\sqrt{5}i}{10}$ when $±$ is plus.

$$m=\frac{3\sqrt{5}i}{5}$$

Now solve the equation $m=\frac{0±6\sqrt{5}i}{10}$ when $±$ is minus.

$$m=-\frac{3\sqrt{5}i}{5}$$

The equation is now solved.

$$m=\frac{3\sqrt{5}i}{5}$$ $$m=-\frac{3\sqrt{5}i}{5}$$