1. **State the problem:** Simplify and solve the expression $$2(x^2 + x - 4)^2 - 4 + \frac{1}{16}$$. 2. **Rewrite the expression:** $$2(x^2 + x - 4)^2 - 4 + \frac{1}{16} = 2(x^2 + x - 4)^2 - \frac{64}{16} + \frac{1}{16}$$ 3. **Combine constants:** $$- \frac{64}{16} + \frac{1}{16} = -\frac{63}{16}$$ 4. **Expression becomes:** $$2(x^2 + x - 4)^2 - \frac{63}{16}$$ 5. **Expand the square:** $$(x^2 + x - 4)^2 = (x^2)^2 + 2 \cdot x^2 \cdot x + 2 \cdot x^2 \cdot (-4) + x^2 + 2 \cdot x \cdot (-4) + (-4)^2$$ More simply, use formula $$(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$$ with $a=x^2$, $b=x$, $c=-4$: $$= x^4 + x^2 + 16 + 2x^3 - 8x^2 - 8x$$ 6. **Simplify inside:** $$x^4 + 2x^3 + (x^2 - 8x^2) - 8x + 16 = x^4 + 2x^3 - 7x^2 - 8x + 16$$ 7. **Multiply by 2:** $$2(x^4 + 2x^3 - 7x^2 - 8x + 16) = 2x^4 + 4x^3 - 14x^2 - 16x + 32$$ 8. **Final expression:** $$2x^4 + 4x^3 - 14x^2 - 16x + 32 - \frac{63}{16}$$ 9. **Combine constants:** $$32 = \frac{512}{16}$$ $$\frac{512}{16} - \frac{63}{16} = \frac{449}{16}$$ 10. **Simplified expression:** $$2x^4 + 4x^3 - 14x^2 - 16x + \frac{449}{16}$$ **Answer:** The simplified form of the expression is $$2x^4 + 4x^3 - 14x^2 - 16x + \frac{449}{16}$$.