Solutions
Solutions to Try Its
1. [latex]\left(x - 6\right)\left(x+1\right)=0;x=6,x=-1[/latex] 2. [latex]\left(x - 7\right)\left(x+3\right)=0[/latex], [latex]x=7[/latex], [latex]x=-3[/latex]. 3. [latex]\left(x+5\right)\left(x - 5\right)=0[/latex], [latex]x=-5[/latex], [latex]x=5[/latex]. 4. [latex]\left(3x+2\right)\left(4x+1\right)=0[/latex], [latex]x=-\frac{2}{3}[/latex], [latex]x=-\frac{1}{4}[/latex] 5. [latex]x=0,x=-10,x=-1[/latex] 6. [latex]x=4\pm \sqrt{5}[/latex] 7. [latex]x=3\pm \sqrt{22}[/latex] 8. [latex]x=-\frac{2}{3}[/latex], [latex]x=\frac{1}{3}[/latex] 9. [latex]5[/latex] unitsSolutions to Odd-Numbered Exercises
1. It is a second-degree equation (the highest variable exponent is 2). 3. We want to take advantage of the zero property of multiplication in the fact that if [latex]a\cdot b=0[/latex] then it must follow that each factor separately offers a solution to the product being zero: [latex]a=0\text{ }or\text{ b}=0[/latex]. 5. One, when no linear term is present (no x term), such as [latex]{x}^{2}=16[/latex]. Two, when the equation is already in the form [latex]{\left(ax+b\right)}^{2}=d[/latex]. 7. [latex]x=6[/latex], [latex]x=3[/latex] 9. [latex]x=\frac{-5}{2}[/latex], [latex]x=\frac{-1}{3}[/latex] 11. [latex]x=5[/latex], [latex]x=-5[/latex] 13. [latex]x=\frac{-3}{2}[/latex], [latex]x=\frac{3}{2}[/latex] 15. [latex]x=-2[/latex] 17. [latex]x=0[/latex], [latex]x=\frac{-3}{7}[/latex] 19. [latex]x=-6[/latex], [latex]x=6[/latex] 21. [latex]x=6[/latex], [latex]x=-4[/latex] 23. [latex]x=1[/latex], [latex]x=-2[/latex] 25. [latex]x=-2[/latex], [latex]x=11[/latex] 27. [latex]x=3\pm \sqrt{22}[/latex] 29. [latex]z=\frac{2}{3}\\[/latex], [latex]z=-\frac{1}{2}[/latex] 31. [latex]x=\frac{3\pm \sqrt{17}}{4}[/latex] 33. Not real 35. One rational 37. Two real; rational 39. [latex]x=\frac{-1\pm \sqrt{17}}{2}[/latex] 41. [latex]x=\frac{5\pm \sqrt{13}}{6}[/latex] 43. [latex]x=\frac{-1\pm \sqrt{17}}{8}[/latex] 45. [latex]x\approx 0.131[/latex] and [latex]x\approx 2.535[/latex] 47. [latex]x\approx -6.7[/latex] and [latex]x\approx 1.7[/latex] 49. [latex]\begin{array}{l}a{x}^{2}+bx+c \hfill& =0\hfill \\ {x}^{2}+\frac{b}{a}x \hfill& =\frac{-c}{a}\hfill \\ {x}^{2}+\frac{b}{a}x+\frac{{b}^{2}}{4{a}^{2}} \hfill& =\frac{-c}{a}+\frac{b}{4{a}^{2}}\hfill \\ {\left(x+\frac{b}{2a}\right)}^{2}\hfill& =\frac{{b}^{2}-4ac}{4{a}^{2}}\hfill \\ x+\frac{b}{2a}\hfill& =\pm \sqrt{\frac{{b}^{2}-4ac}{4{a}^{2}}}\hfill \\ x\hfill& =\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}\hfill \end{array}[/latex] 51. [latex]x\left(x+10\right)=119[/latex]; 7 ft. and 17 ft. 53. maximum at [latex]x=70[/latex] 55. The quadratic equation would be [latex]\left(100x - 0.5{x}^{2}\right)-\left(60x+300\right)=300[/latex]. The two values of [latex]x[/latex] are 20 and 60. 57. 3 feetLicenses & Attributions
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