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目/类型一/ 用直接开平方法解方程
1. $x^2 - 10 = 0$.
2. $(x - 2)^2 = 9$.
3. $4(2x - 3)^2 = 25$.
4. $(x + 1)^2 = 4(x - 2)^2$.
5. $(x + 3)^2 - 25 = 0$.
6. $\frac{7}{5}(3x + 1)^2 = 7$.
目/类型二/ 用配方法解方程
7. $x^2 + 4x - 1 = 0$.
8. $x^2 - 3x + 2 = 0$.
9. $x^2 + 2x = 3$.
10. $x^2 - 2\sqrt{5}x = 4$.
11. $3x^2 - 6x + 4 = 0$.
12. $y^2 + 2\sqrt{3}y - 4 = 0$.
1. $x^2 - 10 = 0$.
2. $(x - 2)^2 = 9$.
3. $4(2x - 3)^2 = 25$.
4. $(x + 1)^2 = 4(x - 2)^2$.
5. $(x + 3)^2 - 25 = 0$.
6. $\frac{7}{5}(3x + 1)^2 = 7$.
目/类型二/ 用配方法解方程
7. $x^2 + 4x - 1 = 0$.
8. $x^2 - 3x + 2 = 0$.
9. $x^2 + 2x = 3$.
10. $x^2 - 2\sqrt{5}x = 4$.
11. $3x^2 - 6x + 4 = 0$.
12. $y^2 + 2\sqrt{3}y - 4 = 0$.
答案
解：移项，得$x^{2}=10，$开方，得$x = \pm\sqrt{10}，$解得$x_1=\sqrt{10},x_2=-\sqrt{10}。$
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解：开方，得$x - 2 = \pm3，$解得$x_1 = 5,x_2 = -1。$
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解：系数化为1，得$(2x - 3)^{2}=\frac{25}{4}，$开方，得$2x - 3 = \pm\frac{5}{2}，$解得$x_1=\frac{11}{4},x_2=\frac{1}{4}。$
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解：原方程可化为$(x + 1)^{2}=[2(x - 2)]^{2}，$$\therefore x + 1 = \pm2(x - 2)，$即$x + 1 = 2x - 4$或$x + 1 = -2x + 4，$解得$x_1 = 5,x_2 = 1。$
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解：移项，得$(x + 3)^{2}=25，$开方，得$x + 3 = \pm5，$解得$x_1 = 2,x_2 = -8。$
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解：原方程可化为$(3x + 1)^{2}=5，$开方，得$3x + 1 = \pm\sqrt{5}，$解得$x_1=\frac{\sqrt{5}-1}{3},x_2=\frac{-\sqrt{5}-1}{3}。$
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解：移项，得$x^{2}+4x = 1$配方，得$x^{2}+4x + 4 = 1 + 4$即$(x + 2)^{2}=5$开方，得$x + 2 = \pm\sqrt{5}$解得$x_1=-2+\sqrt{5},x_2=-2-\sqrt{5}。$
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解：移项，得$x^{2}-3x=-2，$配方，得$x^{2}-3x+\frac{9}{4}=-2+\frac{9}{4}，$即$(x-\frac{3}{2})^{2}=\frac{1}{4}，$开方，得$x-\frac{3}{2}=\pm\frac{1}{2}，$解得$x_1 = 2,x_2 = 1。$
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解：配方，得$x^{2}+2x + 1 = 3 + 1，$即$(x + 1)^{2}=4，$开方，得$x + 1 = \pm2，$解得$x_1 = 1,x_2 = -3。$
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解：配方，得$x^{2}-2\sqrt{5}x + 5 = 4 + 5，$即$(x-\sqrt{5})^{2}=9，$开方，得$x-\sqrt{5}=\pm3，$解得$x_1=\sqrt{5}+3,x_2=\sqrt{5}-3。$
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解：移项，得$3x^{2}-6x=-4，$系数化为1，得$x^{2}-2x=-\frac{4}{3}，$配方，得$x^{2}-2x + 1=-\frac{4}{3}+1，$即$(x - 1)^{2}=-\frac{1}{3}，$$\therefore$原方程无实数解。
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解：移项，得$y^{2}+2\sqrt{3}y = 4，$配方，得$y^{2}+2\sqrt{3}y + 3 = 4 + 3，$即$(y+\sqrt{3})^{2}=7，$开方，得$y+\sqrt{3}=\pm\sqrt{7}，$解得$y_1=-\sqrt{3}+\sqrt{7},y_2=-\sqrt{3}-\sqrt{7}。$
/类型三/ 用公式法解方程
13. $4x^2 + x - 3 = 0$.
14. $3x^2 + 1 = 2\sqrt{3}x$.
15. $2x^2 + 3x + 4 = 0$.
16. $x^2 - 4x + 1 = 0$.
17. $(x+1)(x-1) = 2\sqrt{2}x$.
18. $2x(x-3) = -6x + 5$.
/类型四/ 用因式分解法解方程
19. $(2x-3)(x+1) = 0$.
20. $2x^2 + 3x = 0$.
21. $x^2 - 8x + 7 = 0$.
22. $3x^2 - x(x+6) = 20$.
23. $(x+1) - 2(x^2 - 1) = 0$.
24. $(x-2)^2 = (2x-1)(x-2)$.
/类型五/ 用适当的方法解方程
25. $(2x+1)^2 - 25 = 0$.
26. $x^2 - 2x - 8 = 0$.
27. $2x(x-1) + 3(x-1) = 0$.
28. $(x-3)^2 = (2x+1)^2$.
29. $9(2x-5)^2 - 4 = 0$.
30. $2x^2 - 4\sqrt{5}x = 8$.
31. $3x(x-3) = 2(x-1)(x+1)$.
32. $(x-2)^2 + 4(x-2) - 5 = 0$.
13. $4x^2 + x - 3 = 0$.
14. $3x^2 + 1 = 2\sqrt{3}x$.
15. $2x^2 + 3x + 4 = 0$.
16. $x^2 - 4x + 1 = 0$.
17. $(x+1)(x-1) = 2\sqrt{2}x$.
18. $2x(x-3) = -6x + 5$.
/类型四/ 用因式分解法解方程
19. $(2x-3)(x+1) = 0$.
20. $2x^2 + 3x = 0$.
21. $x^2 - 8x + 7 = 0$.
22. $3x^2 - x(x+6) = 20$.
23. $(x+1) - 2(x^2 - 1) = 0$.
24. $(x-2)^2 = (2x-1)(x-2)$.
/类型五/ 用适当的方法解方程
25. $(2x+1)^2 - 25 = 0$.
26. $x^2 - 2x - 8 = 0$.
27. $2x(x-1) + 3(x-1) = 0$.
28. $(x-3)^2 = (2x+1)^2$.
29. $9(2x-5)^2 - 4 = 0$.
30. $2x^2 - 4\sqrt{5}x = 8$.
31. $3x(x-3) = 2(x-1)(x+1)$.
32. $(x-2)^2 + 4(x-2) - 5 = 0$.
答案
解：$a = 4,b = 1,c=-3，$$b^{2}-4ac = 1^{2}-4\times4\times(-3)=49＞0，$$\therefore x=\frac{-1\pm\sqrt{49}}{2\times4}=\frac{-1\pm7}{8}，$$\therefore x_1=\frac{3}{4},x_2=-1。$
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解：原方程可化为$3x^{2}-2\sqrt{3}x + 1 = 0，$$a = 3,b=-2\sqrt{3},c = 1，$$b^{2}-4ac=(-2\sqrt{3})^{2}-4\times3\times1 = 0，$$\therefore x_1 = x_2=\frac{\sqrt{3}}{3}。$
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解：$a = 2,b = 3,c = 4，$$b^{2}-4ac = 3^{2}-4\times2\times4=-23＜0，$$\therefore$原方程无实数解。
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解：$a = 1,b=-4,c = 1，$$b^{2}-4ac=(-4)^{2}-4\times1\times1 = 12，$$\therefore x=\frac{4\pm2\sqrt{3}}{2}=2\pm\sqrt{3}，$$\therefore x_1=2+\sqrt{3},x_2=2-\sqrt{3}。$
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解：原方程可化为$x^{2}-2\sqrt{2}x - 1 = 0，$$a = 1,b=-2\sqrt{2},c=-1，$$b^{2}-4ac=(-2\sqrt{2})^{2}-4\times1\times(-1)=12＞0，$$\therefore x=\frac{2\sqrt{2}\pm\sqrt{12}}{2}=\sqrt{2}\pm\sqrt{3}，$$\therefore x_1=\sqrt{2}+\sqrt{3},x_2=\sqrt{2}-\sqrt{3}。$
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解：原方程可化为$2x^{2}-5 = 0，$$a = 2,b = 0,c=-5，$$b^{2}-4ac=0^{2}-4\times2\times(-5)=40＞0，$$\therefore x=\frac{0\pm\sqrt{40}}{2\times2}，$$\therefore x_1=\frac{\sqrt{10}}{2},x_2=-\frac{\sqrt{10}}{2}。$
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解：$2x - 3 = 0$或$x + 1 = 0，$$\therefore x_1=\frac{3}{2},x_2=-1。$
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解：因式分解，得$x(2x + 3)=0，$$\therefore x = 0$或$2x + 3 = 0，$$\therefore x_1 = 0,x_2=-\frac{3}{2}。$
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解：因式分解，得$(x - 1)(x - 7)=0，$$\therefore x - 1 = 0$或$x - 7 = 0，$$\therefore x_1 = 1,x_2 = 7。$
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解：原方程可化为$x^{2}-3x - 10 = 0，$因式分解，得$(x - 5)(x + 2)=0，$$\therefore x - 5 = 0$或$x + 2 = 0，$$\therefore x_1 = 5,x_2=-2。$
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解：因式分解，得$(x + 1)[1 - 2(x - 1)]=0，$即$(x + 1)(3 - 2x)=0，$$\therefore x + 1 = 0$或$3 - 2x = 0，$$\therefore x_1=-1,x_2=\frac{3}{2}。$
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解：移项，得$(x - 2)^{2}-(2x - 1)(x - 2)=0，$因式分解，得$(x - 2)(x - 2 - 2x + 1)=0，$即$(x - 2)(-x - 1)=0，$$\therefore x - 2 = 0$或$-x - 1 = 0，$$\therefore x_1 = 2,x_2=-1。$
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解：移项，得$(2x + 1)^{2}=25，$开方，得$2x + 1 = \pm5，$$\therefore x_1 = 2,x_2=-3。$
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解：因式分解，得$(x - 4)(x + 2)=0，$$\therefore x - 4 = 0$或$x + 2 = 0，$$\therefore x_1 = 4,x_2=-2。$
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解：因式分解，得$(2x + 3)(x - 1)=0，$$\therefore 2x + 3 = 0$或$x - 1 = 0，$$\therefore x_1=-\frac{3}{2},x_2 = 1。$
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解：移项，得$(x - 3)^{2}-(2x + 1)^{2}=0，$因式分解，得$(3x - 2)(-x - 4)=0，$$\therefore 3x - 2 = 0$或$-x - 4 = 0，$$\therefore x_1=\frac{2}{3},x_2=-4。$
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解：原方程可化为$(2x - 5)^{2}=\frac{4}{9}，$开方，得$2x - 5 = \pm\frac{2}{3}，$$\therefore x_1=\frac{17}{6},x_2=\frac{13}{6}。$
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解：移项，得$2x^{2}-4\sqrt{5}x - 8 = 0，$$a = 2,b=-4\sqrt{5},c=-8，$$b^{2}-4ac=(-4\sqrt{5})^{2}-4\times2\times(-8)=144，$$\therefore x=\frac{4\sqrt{5}\pm12}{4}=\sqrt{5}\pm3，$$\therefore x_1=\sqrt{5}+3,x_2=\sqrt{5}-3。$
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解：原方程可化为$x^{2}-9x + 2 = 0，$$a = 1,b=-9,c = 2，$$b^{2}-4ac=(-9)^{2}-4\times1\times2 = 73，$$\therefore x=\frac{9\pm\sqrt{73}}{2}，$$\therefore x_1=\frac{9+\sqrt{73}}{2},x_2=\frac{9-\sqrt{73}}{2}。$
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解：因式分解，得$(x - 2 - 1)(x - 2 + 5)=0，$即$(x - 3)(x + 3)=0，$$\therefore x - 3 = 0$或$x + 3 = 0，$$\therefore x_1 = 3,x_2=-3。$
