Solve d = (2a) ^ 2 - 4X1X - (4l ^ 2 - a ^ 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

$$d=(2a)^{2}-4X1X-(4l^{2}-a^{2})$$

Solve for X

$\left\{\begin{matrix}X=\frac{5a^{2}-d-4l^{2}}{4X_{1}}\text{, }&X_{1}\neq 0\\X\in \mathrm{R}\text{, }&d=5a^{2}-4l^{2}\text{ and }X_{1}=0\end{matrix}\right.$

Steps for Solving Linear Equation

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

$$d=2^{2}a^{2}-4X_{1}X-\left(4l^{2}-a^{2}\right)$$

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

$$d=4a^{2}-4X_{1}X-\left(4l^{2}-a^{2}\right)$$

To find the opposite of $4l^{2}-a^{2}$, find the opposite of each term.

$$d=4a^{2}-4X_{1}X-4l^{2}+a^{2}$$

Combine $4a^{2}$ and $a^{2}$ to get $5a^{2}$.

$$d=5a^{2}-4X_{1}X-4l^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$5a^{2}-4X_{1}X-4l^{2}=d$$

Subtract $5a^{2}$ from both sides.

$$-4X_{1}X-4l^{2}=d-5a^{2}$$

Add $4l^{2}$ to both sides.

$$-4X_{1}X=d-5a^{2}+4l^{2}$$

The equation is in standard form.

$$\left(-4X_{1}\right)X=4l^{2}+d-5a^{2}$$

Divide both sides by $-4X_{1}$.

$$\frac{\left(-4X_{1}\right)X}{-4X_{1}}=\frac{4l^{2}+d-5a^{2}}{-4X_{1}}$$

Dividing by $-4X_{1}$ undoes the multiplication by $-4X_{1}$.

$$X=\frac{4l^{2}+d-5a^{2}}{-4X_{1}}$$

Divide $d-5a^{2}+4l^{2}$ by $-4X_{1}$.

$$X=-\frac{4l^{2}+d-5a^{2}}{4X_{1}}$$

Solve for X_1

$\left\{\begin{matrix}X_{1}=\frac{5a^{2}-d-4l^{2}}{4X}\text{, }&X\neq 0\\X_{1}\in \mathrm{R}\text{, }&d=5a^{2}-4l^{2}\text{ and }X=0\end{matrix}\right.$

Steps for Solving Linear Equation

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

$$d=2^{2}a^{2}-4X_{1}X-\left(4l^{2}-a^{2}\right)$$

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

$$d=4a^{2}-4X_{1}X-\left(4l^{2}-a^{2}\right)$$

To find the opposite of $4l^{2}-a^{2}$, find the opposite of each term.

$$d=4a^{2}-4X_{1}X-4l^{2}+a^{2}$$

Combine $4a^{2}$ and $a^{2}$ to get $5a^{2}$.

$$d=5a^{2}-4X_{1}X-4l^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$5a^{2}-4X_{1}X-4l^{2}=d$$

Subtract $5a^{2}$ from both sides.

$$-4X_{1}X-4l^{2}=d-5a^{2}$$

Add $4l^{2}$ to both sides.

$$-4X_{1}X=d-5a^{2}+4l^{2}$$

The equation is in standard form.

$$\left(-4X\right)X_{1}=4l^{2}+d-5a^{2}$$

Divide both sides by $-4X$.

$$\frac{\left(-4X\right)X_{1}}{-4X}=\frac{4l^{2}+d-5a^{2}}{-4X}$$

Dividing by $-4X$ undoes the multiplication by $-4X$.

$$X_{1}=\frac{4l^{2}+d-5a^{2}}{-4X}$$

Divide $d-5a^{2}+4l^{2}$ by $-4X$.

$$X_{1}=-\frac{4l^{2}+d-5a^{2}}{4X}$$