Solve 25(x)^(2)(y)^(2)=144(x)^(2)(y)^(2) | 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

$$25 { x }^{ 2 } { y }^{ 2 } =144 { x }^{ 2 } { y }^{ 2 }$$

Solve for x (complex solution)

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $144x^{2}y^{2}$ from both sides.

$$25x^{2}y^{2}-144x^{2}y^{2}=0$$

Combine $25x^{2}y^{2}$ and $-144x^{2}y^{2}$ to get $-119x^{2}y^{2}$.

$$-119x^{2}y^{2}=0$$

Dividing by $-119y^{2}$ undoes the multiplication by $-119y^{2}$.

$$x^{2}=\frac{0}{-119y^{2}}$$

Divide $0$ by $-119y^{2}$.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0$$ $$x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Subtract $144x^{2}y^{2}$ from both sides.

$$25x^{2}y^{2}-144x^{2}y^{2}=0$$

Combine $25x^{2}y^{2}$ and $-144x^{2}y^{2}$ to get $-119x^{2}y^{2}$.

$$-119x^{2}y^{2}=0$$

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$\left(-119y^{2}\right)x^{2}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-119y^{2}$ for $a$, $0$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}}}{2\left(-119y^{2}\right)}$$

Take the square root of $0^{2}$.

$$x=\frac{0±0}{2\left(-119y^{2}\right)}$$

Multiply $2$ times $-119y^{2}$.

$$x=\frac{0}{-238y^{2}}$$

Divide $0$ by $-238y^{2}$.

$$x=0$$

Solve for y (complex solution)

$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $144x^{2}y^{2}$ from both sides.

$$25x^{2}y^{2}-144x^{2}y^{2}=0$$

Combine $25x^{2}y^{2}$ and $-144x^{2}y^{2}$ to get $-119x^{2}y^{2}$.

$$-119x^{2}y^{2}=0$$

Dividing by $-119x^{2}$ undoes the multiplication by $-119x^{2}$.

$$y^{2}=\frac{0}{-119x^{2}}$$

Divide $0$ by $-119x^{2}$.

$$y^{2}=0$$

Take the square root of both sides of the equation.

$$y=0$$ $$y=0$$

The equation is now solved. Solutions are the same.

$$y=0$$

Steps Using the Quadratic Formula

Subtract $144x^{2}y^{2}$ from both sides.

$$25x^{2}y^{2}-144x^{2}y^{2}=0$$

Combine $25x^{2}y^{2}$ and $-144x^{2}y^{2}$ to get $-119x^{2}y^{2}$.

$$-119x^{2}y^{2}=0$$

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$\left(-119x^{2}\right)y^{2}=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-119x^{2}$ for $a$, $0$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$y=\frac{0±\sqrt{0^{2}}}{2\left(-119x^{2}\right)}$$

Take the square root of $0^{2}$.

$$y=\frac{0±0}{2\left(-119x^{2}\right)}$$

Multiply $2$ times $-119x^{2}$.

$$y=\frac{0}{-238x^{2}}$$

Divide $0$ by $-238x^{2}$.

$$y=0$$

Solve for x

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$

Solve for y

$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$