Solve for d q = square root of Fd+4

$q = \sqrt{F d + 4}$

Step 1

Rewrite the equation as $\sqrt{F d + 4} = q$ .

$\sqrt{F d + 4} = q$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{F d + 4}}^{2} = q^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{F d + 4}$ as ${(F d + 4)}^{\frac{1}{2}}$ .

${({(F d + 4)}^{\frac{1}{2}})}^{2} = q^{2}$

Simplify the left side.

Simplify ${({(F d + 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(F d + 4)}^{\frac{1}{2}})}^{2}$ .

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

${(F d + 4)}^{\frac{1}{2} \cdot 2} = q^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(F d + 4)}^{\frac{1}{2} \cdot 2} = q^{2}$

Rewrite the expression.

${(F d + 4)}^{1} = q^{2}$

Simplify.

$F d + 4 = q^{2}$

Step 4

Solve for $d$ .

Subtract $4$ from both sides of the equation.

$F d = q^{2} - 4$

Divide each term in $F d = q^{2} - 4$ by $F$ and simplify.

Divide each term in $F d = q^{2} - 4$ by $F$ .

$\frac{F d}{F} = \frac{q^{2}}{F} + \frac{- 4}{F}$

Simplify the left side.

Cancel the common factor of $F$ .

Cancel the common factor.

$\frac{F d}{F} = \frac{q^{2}}{F} + \frac{- 4}{F}$

Divide $d$ by $1$ .

$d = \frac{q^{2}}{F} + \frac{- 4}{F}$

Simplify the right side.

Move the negative in front of the fraction.

$d = \frac{q^{2}}{F} - \frac{4}{F}$