Quadratic Equations

1. [latex]x=6[/latex], [latex]x=3[/latex]
2. [latex]x=-\dfrac{5}{2}[/latex], [latex]x=-\dfrac{1}{3}[/latex]
3. [latex]x=5[/latex], [latex]x=-5[/latex]
4. [latex]x=-\dfrac{3}{2}[/latex], [latex]x=\dfrac{3}{2}[/latex]
5. [latex]x=-2[/latex], [latex]x=3[/latex]
6. [latex]x=0[/latex], [latex]x=-\dfrac{3}{7}[/latex]
7. [latex]x=-6[/latex], [latex]x=6[/latex]
8. [latex]x=6[/latex], [latex]x=-4[/latex]
9. [latex]x=1[/latex], [latex]x=-2[/latex]
10. [latex]x=-2[/latex], [latex]x=11[/latex]
11. [latex]x=3\pm\sqrt{22}[/latex]
12. [latex]z=\dfrac{2}{3}[/latex], [latex]z=-\dfrac{1}{2}[/latex]
13. [latex]x=\dfrac{3+\sqrt{17}}{4}[/latex]
14. Not real
15. One rational
16. Two real; rational
17. [latex]x=\dfrac{-1\pm\sqrt{17}}{2}[/latex]
18. [latex]x=\dfrac{5\pm\sqrt{13}}{6}[/latex]
19. [latex]x=\dfrac{-1\pm\sqrt{17}}{8}[/latex]
20. [latex](x+\frac{b}{2a})^2=\dfrac{b^2-4ac}{4a^2}[/latex]
    [latex]x+\dfrac{b}{2a}=\pm\sqrt{\dfrac{b^2-4ac}{4a^2}}[/latex]
    [latex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/latex]
21. [latex]x(x+10)=119[/latex]; [latex]7[/latex] ft. and [latex]17[/latex] ft.
22. maximum at [latex]x=70[/latex]
23. The quadratic equation would be [latex](100x-0,5x^2)-(60x+300)=300[/latex]. The two values of [latex]x[/latex] are [latex]20[/latex] and [latex]60[/latex].
24. [latex]3[/latex] feet

Other Types of Equations

1. [latex]x\neq-4[/latex]; [latex]x=-3[/latex]
2. [latex]x\neq1[/latex]; when we solve this we get [latex]x=1[/latex], which is excluded, therefore NO solution
3. [latex]x\neq0[/latex]; [latex]x=-\dfrac{5}{2}[/latex]
4. [latex]x=81[/latex]
5. [latex]x=17[/latex]
6. [latex]x=8[/latex], [latex]x=27[/latex]
7. [latex]x=-2,1,-1[/latex]
8. [latex]y=0,\dfrac{3}{2},-\dfrac{3}{2}[/latex]
9. [latex]m=1,-1[/latex]
10. [latex]x=\dfrac{2}{5},\pm3i[/latex]
11. [latex]x=32[/latex]
12. [latex]t=\dfrac{44}{3}[/latex]
13. [latex]x=3[/latex]
14. [latex]x=-2[/latex]
15. [latex]x=4,-\dfrac{4}{3}[/latex]
16. [latex]x=-\dfrac{5}{4},\dfrac{7}{4}[/latex]
17. [latex]x=3,-2[/latex]
18. [latex]x=-5[/latex]
20. [latex]10[/latex] in.
22. [latex]90[/latex] kg
23. [latex](-\infty,\infty)[/latex]
24. [latex](-\infty,-\dfrac{10}{3})\cup(4,\infty)[/latex]
25. [latex](-\infty,-4]\cup[8,+\infty)[/latex]
26. No solution
27. [latex](-5,11)[/latex]