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Study Guides > College Algebra

Solutions

Solutions to Try Its

1. (x6)(x+1)=0;x=6,x=1\left(x - 6\right)\left(x+1\right)=0;x=6,x=-1 2. (x7)(x+3)=0\left(x - 7\right)\left(x+3\right)=0, x=7x=7, x=3x=-3. 3. (x+5)(x5)=0\left(x+5\right)\left(x - 5\right)=0, x=5x=-5, x=5x=5. 4. (3x+2)(4x+1)=0\left(3x+2\right)\left(4x+1\right)=0, x=23x=-\frac{2}{3}, x=14x=-\frac{1}{4} 5. x=0,x=10,x=1x=0,x=-10,x=-1 6. x=4±5x=4\pm \sqrt{5} 7. x=3±22x=3\pm \sqrt{22} 8. x=23x=-\frac{2}{3}, x=13x=\frac{1}{3} 9. 55 units

Solutions 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 ab=0a\cdot b=0 then it must follow that each factor separately offers a solution to the product being zero: a=0 or b=0a=0\text{ }or\text{ b}=0. 5. One, when no linear term is present (no x term), such as x2=16{x}^{2}=16. Two, when the equation is already in the form (ax+b)2=d{\left(ax+b\right)}^{2}=d. 7. x=6x=6, x=3x=3 9. x=52x=\frac{-5}{2}, x=13x=\frac{-1}{3} 11. x=5x=5, x=5x=-5 13. x=32x=\frac{-3}{2}, x=32x=\frac{3}{2} 15. x=2x=-2 17. x=0x=0, x=37x=\frac{-3}{7} 19. x=6x=-6, x=6x=6 21. x=6x=6, x=4x=-4 23. x=1x=1, x=2x=-2 25. x=2x=-2, x=11x=11 27. x=3±22x=3\pm \sqrt{22} 29. z=23z=\frac{2}{3}\\, z=12z=-\frac{1}{2} 31. x=3±174x=\frac{3\pm \sqrt{17}}{4} 33. Not real 35. One rational 37. Two real; rational 39. x=1±172x=\frac{-1\pm \sqrt{17}}{2} 41. x=5±136x=\frac{5\pm \sqrt{13}}{6} 43. x=1±178x=\frac{-1\pm \sqrt{17}}{8} 45. x0.131x\approx 0.131 and x2.535x\approx 2.535 47. x6.7x\approx -6.7 and x1.7x\approx 1.7 49. ax2+bx+c=0x2+bax=cax2+bax+b24a2=ca+b4a2(x+b2a)2=b24ac4a2x+b2a=±b24ac4a2x=b±b24ac2a\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} 51. x(x+10)=119x\left(x+10\right)=119; 7 ft. and 17 ft. 53. maximum at x=70x=70 55. The quadratic equation would be (100x0.5x2)(60x+300)=300\left(100x - 0.5{x}^{2}\right)-\left(60x+300\right)=300. The two values of xx are 20 and 60. 57. 3 feet

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