Solve H = (7x - 5sqrt(2))(7x + sqrt(50)) = les | 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

$$H = ( 7 x - 5 \sqrt { 2 } ) ( 7 x + \sqrt { 50 } ) \quad I =$$

Solve for I (complex solution)

$\left\{\begin{matrix}I=\frac{H}{49x^{2}-50}\text{, }&x\neq -\frac{5\sqrt{2}}{7}\text{ and }x\neq \frac{5\sqrt{2}}{7}\\I\in \mathrm{C}\text{, }&\left(x=\frac{5\sqrt{2}}{7}\text{ or }x=-\frac{5\sqrt{2}}{7}\right)\text{ and }H=0\end{matrix}\right.$

Steps for Solving Linear Equation

Factor $50=5^{2}\times 2$. Rewrite the square root of the product $\sqrt{5^{2}\times 2}$ as the product of square roots $\sqrt{5^{2}}\sqrt{2}$. Take the square root of $5^{2}$.

$$H=\left(7x-5\sqrt{2}\right)\left(7x+5\sqrt{2}\right)I$$

Use the distributive property to multiply $7x-5\sqrt{2}$ by $7x+5\sqrt{2}$ and combine like terms.

$$H=\left(49x^{2}-25\left(\sqrt{2}\right)^{2}\right)I$$

The square of $\sqrt{2}$ is $2$.

$$H=\left(49x^{2}-25\times 2\right)I$$

Multiply $-25$ and $2$ to get $-50$.

$$H=\left(49x^{2}-50\right)I$$

Use the distributive property to multiply $49x^{2}-50$ by $I$.

$$H=49x^{2}I-50I$$

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

$$49x^{2}I-50I=H$$

Combine all terms containing $I$.

$$\left(49x^{2}-50\right)I=H$$

Divide both sides by $49x^{2}-50$.

$$\frac{\left(49x^{2}-50\right)I}{49x^{2}-50}=\frac{H}{49x^{2}-50}$$

Dividing by $49x^{2}-50$ undoes the multiplication by $49x^{2}-50$.

$$I=\frac{H}{49x^{2}-50}$$

Solve for I

$\left\{\begin{matrix}I=\frac{H}{49x^{2}-50}\text{, }&|x|\neq \frac{5\sqrt{2}}{7}\\I\in \mathrm{R}\text{, }&H=0\text{ and }|x|=\frac{5\sqrt{2}}{7}\end{matrix}\right.$

Steps for Solving Linear Equation

Factor $50=5^{2}\times 2$. Rewrite the square root of the product $\sqrt{5^{2}\times 2}$ as the product of square roots $\sqrt{5^{2}}\sqrt{2}$. Take the square root of $5^{2}$.

$$H=\left(7x-5\sqrt{2}\right)\left(7x+5\sqrt{2}\right)I$$

Use the distributive property to multiply $7x-5\sqrt{2}$ by $7x+5\sqrt{2}$ and combine like terms.

$$H=\left(49x^{2}-25\left(\sqrt{2}\right)^{2}\right)I$$

The square of $\sqrt{2}$ is $2$.

$$H=\left(49x^{2}-25\times 2\right)I$$

Multiply $-25$ and $2$ to get $-50$.

$$H=\left(49x^{2}-50\right)I$$

Use the distributive property to multiply $49x^{2}-50$ by $I$.

$$H=49x^{2}I-50I$$

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

$$49x^{2}I-50I=H$$

Combine all terms containing $I$.

$$\left(49x^{2}-50\right)I=H$$

Divide both sides by $49x^{2}-50$.

$$\frac{\left(49x^{2}-50\right)I}{49x^{2}-50}=\frac{H}{49x^{2}-50}$$

Dividing by $49x^{2}-50$ undoes the multiplication by $49x^{2}-50$.

$$I=\frac{H}{49x^{2}-50}$$

Solve for H

$H=I\left(49x^{2}-50\right)$