Solve for d T = square root of hd-2Q

$T = \sqrt{h d - 2 Q}$

Rewrite the equation as $\sqrt{h d - 2 Q} = T$ .

$\sqrt{h d - 2 Q} = T$

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

${\sqrt{h d - 2 Q}}^{2} = T^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{h d - 2 Q}$ as ${(h d - 2 Q)}^{\frac{1}{2}}$ .

${({(h d - 2 Q)}^{\frac{1}{2}})}^{2} = T^{2}$

Simplify the left side.

Simplify ${({(h d - 2 Q)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(h d - 2 Q)}^{\frac{1}{2}})}^{2}$ .

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

${(h d - 2 Q)}^{\frac{1}{2} \cdot 2} = T^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(h d - 2 Q)}^{\frac{1}{2} \cdot 2} = T^{2}$

Rewrite the expression.

${(h d - 2 Q)}^{1} = T^{2}$

Simplify.

$h d - 2 Q = T^{2}$

Solve for $d$ .

Add $2 Q$ to both sides of the equation.

$h d = T^{2} + 2 Q$

Divide each term in $h d = T^{2} + 2 Q$ by $h$ and simplify.

Divide each term in $h d = T^{2} + 2 Q$ by $h$ .

$\frac{h d}{h} = \frac{T^{2}}{h} + \frac{2 Q}{h}$

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

$\frac{h d}{h} = \frac{T^{2}}{h} + \frac{2 Q}{h}$

Divide $d$ by $1$ .

$d = \frac{T^{2}}{h} + \frac{2 Q}{h}$