Start by squaring both sides to remove the square root.

$p^{2} = \frac{a c + 8}{3 + c}$

[1]

Remove fractions by multiplying (both sides) by 3 + c.

$p^{2} (3 + c) = a c + 8$

Expand the brackets by multiplying each term inside by p².

$3 p^{2} + c p^{2} = a c + 8$

[1]

Being all the c terms to one side (for example, by subtracting ac from both sides then adding 3p² to both sides)

$\begin{array}{rcl} 3 p^{2} + c p^{2} - a c & = & 8 \\ c p^{2} - a c & = & 8 - 3 p^{2} \end{array}$

[1]

Factorise c from the terms on the left-hand side.

$c (p^{2} - a) = 8 - 3 p^{2}$

Isolate c by dividing (both sides) by p² - a.

$c = \frac{8 - 3 p^{2}}{p^{2} - a}$

There is nothing to simplify or rearrange so this is the final answer.

$c = \frac{8 - 3 p^{2}}{p^{2} - a}$ [1]

Equivalent expressions allowed such as $c = \frac{3 p^{2} - 8}{a - p^{2}}$ .

Rearranging Formula (CIE IGCSE Maths: Extended)

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