Solve A * D ^ 2 + C * D ^ 2 = (sqrt(10)) ^ 2 + (sqrt(10)) ^ 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

$$AD^{2}+CD^{2}=(\sqrt{10})^{2}+(\sqrt{10})^{2}$$

Solve for A

$A=-C+\frac{20}{D^{2}}$
$D\neq 0$

Steps for Solving Linear Equation

The square of $\sqrt{10}$ is $10$.

$$AD^{2}+CD^{2}=10+\left(\sqrt{10}\right)^{2}$$

The square of $\sqrt{10}$ is $10$.

$$AD^{2}+CD^{2}=10+10$$

Add $10$ and $10$ to get $20$.

$$AD^{2}+CD^{2}=20$$

Subtract $CD^{2}$ from both sides.

$$AD^{2}=20-CD^{2}$$

Reorder the terms.

$$AD^{2}=-CD^{2}+20$$

The equation is in standard form.

$$D^{2}A=20-CD^{2}$$

Divide both sides by $D^{2}$.

$$\frac{D^{2}A}{D^{2}}=\frac{20-CD^{2}}{D^{2}}$$

Dividing by $D^{2}$ undoes the multiplication by $D^{2}$.

$$A=\frac{20-CD^{2}}{D^{2}}$$

Divide $-CD^{2}+20$ by $D^{2}$.

$$A=-C+\frac{20}{D^{2}}$$

Solve for C

$C=-A+\frac{20}{D^{2}}$
$D\neq 0$

Steps for Solving Linear Equation

The square of $\sqrt{10}$ is $10$.

$$AD^{2}+CD^{2}=10+\left(\sqrt{10}\right)^{2}$$

The square of $\sqrt{10}$ is $10$.

$$AD^{2}+CD^{2}=10+10$$

Add $10$ and $10$ to get $20$.

$$AD^{2}+CD^{2}=20$$

Subtract $AD^{2}$ from both sides.

$$CD^{2}=20-AD^{2}$$

Reorder the terms.

$$CD^{2}=-AD^{2}+20$$

The equation is in standard form.

$$D^{2}C=20-AD^{2}$$

Divide both sides by $D^{2}$.

$$\frac{D^{2}C}{D^{2}}=\frac{20-AD^{2}}{D^{2}}$$

Dividing by $D^{2}$ undoes the multiplication by $D^{2}$.

$$C=\frac{20-AD^{2}}{D^{2}}$$

Divide $-AD^{2}+20$ by $D^{2}$.

$$C=-A+\frac{20}{D^{2}}$$