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Solve the equation 3p2 - 32 = -5p2 for p.

May 26, 2026Mathematics

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Answer

p = \pm 2

4 steps

Add $5p^2$ to both sides of the equation to gather all $p^2$ terms on one side.
$3p^2 - 32 = -5p^2$ $3p^2 + 5p^2 - 32 = 0$ $8p^2 - 32 = 0$
Add 32 to both sides of the equation to isolate the term with $p^2$ .
$8p^2 = 32$
Divide both sides by 8 to solve for $p^2$ .
$p^2 = \frac{32}{8}$ $p^2 = 4$
Take the square root of both sides to solve for $p$ .
Remember to include both positive and negative roots.
$p = \pm\sqrt{4}$ $p = \pm 2$
The solutions for $p$ are 2 and $-2$ .

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