Solve the equation 2x2 − 72 = 0. Shade (P U Q)' ∩ R on the diagram in the answer space below.

$$2x^2 - 72 + 72 = 0 + 72$$ $$2x^2 = 72$$

$$\frac{2x^2}{2} = \frac{72}{2}$$ $$x^2 = 36$$

Remember to include both the positive and negative roots.

$$\sqrt{x^2} = \pm\sqrt{36}$$ $$x = \pm 6$$

The solutions for $x$ are:

$$\boxed{x = 6 \text{ or } x = -6}$$

5. Shade $(P \cup Q)' \cap R$ on the diagram in the answer space below.

To shade $(P \cup Q)' \cap R$:

• First, identify the region $(P \cup Q)$, which is everything inside circle P or circle Q (or both).
• Next, find $(P \cup Q)'$, which is everything outside of the combined region of P and Q.
• Finally, intersect this region with R, meaning you only consider the parts of $(P \cup Q)'$ that are also inside circle R.

This means you should shade the region that is part of set R, but is not part of set P and not part of set Q. It is the portion of R that does not overlap with P or Q.