$$ \begin{array}{ll} ext { 9. } x^{2}+8 x+16 \ ext { 10. } x^{2}+2 x+1 & = \ ext { 11. } x^{2}+4 x-32 & = \ ext { 13. } x^{2}-3 x-10 & = \ ext { 14. } x^{2}-2 x-3 \ ext { 15. } x^{2}+3 x-4 & = \ ext { 16. } x^{2}-4 x-45 & = \ ext { 17. } x^{2}-3 x-18 \ ext { 18. } x^{2}+2 x-48 \ ext { 19. } & = \ ext { 20. } x^{2}-3 x-4 & =\end{array} $$

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$$ \begin{array}{ll}	ext { 9. } x^{2}+8 x+16 \ 	ext { 10. } x^{2}+2 x+1 & = \ 	ext { 11. } x^{2}+4 x-32 & = \ 	ext { 13. } x^{2}-3 x-10 & = \ 	ext { 14. } x^{2}-2 x-3 \ 	ext { 15. } x^{2}+3 x-4 & = \ 	ext { 16. } x^{2}-4 x-45 & = \ 	ext { 17. } x^{2}-3 x-18 \ 	ext { 18. } x^{2}+2 x-48 \ 	ext { 19. } & = \ 	ext { 20. } x^{2}-3 x-4 & =\end{array} $$

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Alright, I need to solve these quadratic equations. Let's start by looking at each one individually.

First, equation 9: $$ x^{2} + 8x + 16 $$. Hmm, this looks like a perfect square trinomial. Let me check if it fits the form $$ (x + a)^2 = x^2 + 2ax + a^2 $$. Comparing, $$ 2a = 8 $$, so $$ a = 4 $$. Therefore, $$ x^2 + 8x + 16 = (x + 4)^2 $$. So, the solution is $$ x = -4 $$.

Moving on to equation 10: $$ x^{2} + 2x + 1 $$. This is also a perfect square trinomial. Comparing, $$ 2a = 2 $$, so $$ a = 1 $$. Thus, $$ x^2 + 2x + 1 = (x + 1)^2 $$. The solution is $$ x = -1 $$.

Next, equation 11: $$ x^{2} + 4x - 32 $$. This doesn't seem to be a perfect square, so I'll try factoring. I need two numbers that multiply to -32 and add up to 4. Let's see, 8 and -4 multiply to -32 and add up to 4. So, $$ x^2 + 4x - 32 = (x + 8)(x - 4) $$. Setting each factor to zero gives $$ x = -8 $$ and $$ x = 4 $$.

Equation 13: $$ x^{2} - 3x - 10 $$. Again, not a perfect square. I'll try factoring. I need two numbers that multiply to -10 and add up to -3. The numbers 2 and -5 fit this: 2 * -5 = -10 and 2 + (-5) = -3. So, $$ x^2 - 3x - 10 = (x + 2)(x - 5) $$. Setting each factor to zero gives $$ x = -2 $$ and $$ x = 5 $$.

Equation 14: $$ x^{2} - 2x - 3 $$. Not a perfect square. Factoring, I need two numbers that multiply to -3 and add up to -2. The numbers 1 and -3 fit: 1 * -3 = -3 and 1 + (-3) = -2. So, $$ x^2 - 2x - 3 = (x + 1)(x - 3) $$. Setting each factor to zero gives $$ x = -1 $$ and $$ x = 3 $$.

Equation 15: $$ x^{2} + 3x - 4 $$. Not a perfect square. Factoring, I need two numbers that multiply to -4 and add up to 3. The numbers 4 and -1 fit: 4 * -1 = -4 and 4 + (-1) = 3. So, $$ x^2 + 3x - 4 = (x + 4)(x - 1) $$. Setting each factor to zero gives $$ x = -4 $$ and $$ x = 1 $$.

Equation 16: $$ x^{2} - 4x - 45 $$. Not a perfect square. Factoring, I need two numbers that multiply to -45 and add up to -4. The numbers 9 and -5 fit: 9 * -5 = -45 and 9 + (-5) = 4. Wait, that's 4, not -4. Let me try again. The numbers -9 and 5 fit: -9 * 5 = -45 and -9 + 5 = -4. So, $$ x^2 - 4x - 45 = (x - 9)(x + 5) $$. Setting each factor to zero gives $$ x = 9 $$ and $$ x = -5 $$.

Equation 17: $$ x^{2} - 3x - 18 $$. Not a perfect square. Factoring, I need two numbers that multiply to -18 and add up to -3. The numbers 3 and -6 fit: 3 * -6 = -18 and 3 + (-6) = -3. So, $$ x^2 - 3x - 18 = (x + 3)(x - 6) $$. Setting each factor to zero gives $$ x = -3 $$ and $$ x = 6 $$.

Equation 18: $$ x^{2} + 2x - 48 $$. Not a perfect square. Factoring, I need two numbers that multiply to -48 and add up to 2. The numbers 8 and -6 fit: 8 * -6 = -48 and 8 + (-6) = 2. So, $$ x^2 + 2x - 48 = (x + 8)(x - 6) $$. Setting each factor to zero gives $$ x = -8 $$ and $$ x = 6 $$.

Equation 19: It seems to be missing. Maybe it's a typo or an incomplete equation. I'll skip this one for now.

Equation 20: $$ x^{2} - 3x - 4 $$. Not a perfect square. Factoring, I need two numbers that multiply to -4 and add up to -3. The numbers 1 and -4 fit: 1 * -4 = -4 and 1 + (-4) = -3. So, $$ x^2 - 3x - 4 = (x + 1)(x - 4) $$. Setting each factor to zero gives $$ x = -1 $$ and $$ x = 4 $$.

9. $$ x = -4 $$ 10. $$ x = -1 $$ 11. $$ x = -8 $$ and $$ x = 4 $$ 13. $$ x = -2 $$ and $$ x = 5 $$ 14. $$ x = -1 $$ and $$ x = 3 $$ 15. $$ x = -4 $$ and $$ x = 1 $$ 16. $$ x = 9 $$ and $$ x = -5 $$ 17. $$ x = -3 $$ and $$ x = 6 $$ 18. $$ x = -8 $$ and $$ x = 6 $$ 20. $$ x = -1 $$ and $$ x = 4 $$

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