Solve for F HF^2+n=q

$H F^{2} + n = q$

Step 1

Subtract $n$ from both sides of the equation.

$H F^{2} = q - n$

Step 2

Divide each term in $H F^{2} = q - n$ by $H$ and simplify.

Divide each term in $H F^{2} = q - n$ by $H$ .

$\frac{H F^{2}}{H} = \frac{q}{H} + \frac{- n}{H}$

Simplify the left side.

Cancel the common factor of $H$ .

Cancel the common factor.

$\frac{H F^{2}}{H} = \frac{q}{H} + \frac{- n}{H}$

Divide $F^{2}$ by $1$ .

$F^{2} = \frac{q}{H} + \frac{- n}{H}$

Simplify the right side.

Move the negative in front of the fraction.

$F^{2} = \frac{q}{H} - \frac{n}{H}$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$F = \pm \sqrt{\frac{q}{H} - \frac{n}{H}}$

Step 4

Simplify $\pm \sqrt{\frac{q}{H} - \frac{n}{H}}$ .

Combine the numerators over the common denominator.

$F = \pm \sqrt{\frac{q - n}{H}}$

Rewrite $\sqrt{\frac{q - n}{H}}$ as $\frac{\sqrt{q - n}}{\sqrt{H}}$ .

$F = \pm \frac{\sqrt{q - n}}{\sqrt{H}}$

Multiply $\frac{\sqrt{q - n}}{\sqrt{H}}$ by $\frac{\sqrt{H}}{\sqrt{H}}$ .

$F = \pm \frac{\sqrt{q - n}}{\sqrt{H}} \cdot \frac{\sqrt{H}}{\sqrt{H}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{q - n}}{\sqrt{H}}$ by $\frac{\sqrt{H}}{\sqrt{H}}$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{\sqrt{H} \sqrt{H}}$

Raise $\sqrt{H}$ to the power of $1$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{{\sqrt{H}}^{1} \sqrt{H}}$

Raise $\sqrt{H}$ to the power of $1$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{{\sqrt{H}}^{1} {\sqrt{H}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{{\sqrt{H}}^{1 + 1}}$

Add $1$ and $1$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{{\sqrt{H}}^{2}}$

Rewrite ${\sqrt{H}}^{2}$ as $H$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{H}$ as $H^{\frac{1}{2}}$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{{(H^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{H^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{H^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{H^{\frac{2}{2}}}$

Rewrite the expression.

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{H^{1}}$

Simplify.

$F = \pm \frac{\sqrt{q - n} \sqrt{H}}{H}$

Combine using the product rule for radicals.

$F = \pm \frac{\sqrt{(q - n) H}}{H}$

Reorder factors in $\pm \frac{\sqrt{(q - n) H}}{H}$ .

$F = \pm \frac{\sqrt{H (q - n)}}{H}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$F = \frac{\sqrt{H (q - n)}}{H}$

Next, use the negative value of the $\pm$ to find the second solution.

$F = - \frac{\sqrt{H (q - n)}}{H}$

The complete solution is the result of both the positive and negative portions of the solution.

$F = \frac{\sqrt{H (q - n)}}{H}$

$F = - \frac{\sqrt{H (q - n)}}{H}$

$F = \frac{\sqrt{H (q - n)}}{H}$

$F = - \frac{\sqrt{H (q - n)}}{H}$

Solve for F HF^2+n=q

Related Questions

Support LCMGCF.com by disabling your adblocker.