1.[tex](2x - 3)(x + 7) = 0[/tex]
[tex]2x^{2} + 14x - 3x - 21 = 0[/tex]
[tex]2x^{2} + 11x - 21 = 0[/tex]
[tex]x = \frac{-11 +/- \sqrt{11^{2} - 4(2)(-21)}}{2(2)} [/tex]
[tex]x = \frac{-11 +/- \sqrt{121 + 168}}{4} [/tex]
[tex]x = \frac{-11 +/- \sqrt{289}}{4} [/tex]
[tex]x = \frac{-11 +/- 17}{4} [/tex]
[tex]x = -2.75 +/- 4.25[/tex]
[tex]x = -2.75 + 4.25[/tex] [tex]x = -2.75 - 4.25[/tex]
[tex]x = 1.5[/tex] [tex]x = -7[/tex]
---------------------------------------------------------------------------------------------------------- 2.[tex]8x(2x - 5) = 0[/tex]
[tex]8x(2x) - 8x(5) = 0[/tex]
[tex]16x^{2} - 40x = 0[/tex]
[tex]16x^{2} - 4x + 0 = 0[/tex]
[tex]x = \frac{-(-40) +/- \sqrt{(-40)^{2} - 4(16)(0)}}{2(16)}[/tex]
[tex]x = \frac{40 +/- \sqrt{1600 - 0}}{32}[/tex]
[tex]x = \frac{40 +/- \sqrt{1600}}{32}[/tex]
[tex]x = \frac{40 +/- 40}{32} [/tex]
[tex]x = 1.25 +/- 1.25[/tex]
[tex]x = 1.25 + 1.25[/tex] [tex]x = 1.25 - 1.25[/tex]
[tex]x = 2.5[/tex] [tex]x = 0[/tex]
----------------------------------------------------------------------------------------------------------
3.[tex]x^{2} + 3x - 10 = 0[/tex]
[tex]x = \frac{-3 +/- \sqrt{3^{2} - 4(1)(-10)}}{2(1)} [/tex]
[tex]x = \frac{-3 +/- \sqrt{9 + 40}}{2} [/tex]
[tex]x = \frac{-3 +/- \sqrt{49}}{2} [/tex]
[tex]x = \frac{-3 +/- {7}}{2} [/tex]
[tex]x = -1.5 +/- 3.5[/tex]
[tex]x = -1.5 + 3.5[/tex] [tex]x = -1.5 - 3.5[/tex]
[tex]x = 2[/tex] [tex]x = -5[/tex]
----------------------------------------------------------------------------------------------------------
4. [tex]x^{2} = 13x - 36[/tex]
[tex]x^{2} - 13x + 36 = 13x - 13x - 36 + 36[/tex]
[tex]x^{2} - 13x + 36 = 0[/tex]
[tex]x = \frac{-(-13) +/- \sqrt{(-13)^{2} - 4(1)(36)}}{2(1)} [/tex]
[tex]x = \frac{13 +/- \sqrt{169 - 144}}{2} [/tex]
[tex]x = \frac{13 +/- \sqrt{25}}{2} [/tex]
[tex]x = \frac{13 +/- 5}{2} [/tex]
[tex]x = 6.5 +/- 2.5[/tex]
[tex]x = 6.5 + 2.5[/tex] [tex]x = 6.5 - 2.5[/tex]
[tex]x = 9[/tex] [tex]x = 4[/tex]
----------------------------------------------------------------------------------------------------------
5.[tex]3x^{2} - 7x + 2 = 0[/tex]
[tex]x = \frac{-(-7) +/- \sqrt{(-7)^{2} - 4(1)(2)}}{2(3)} [/tex]
[tex]x = \frac{7 +/- \sqrt{49 - 8}}{6} [/tex]
[tex]x = \frac{7 +/- \sqrt{41}}{6} [/tex]
[tex]x = \frac{7 +/- 6.403124237432849}{6} [/tex]
[tex]x = 1.167+/- 1.06718737290547[/tex]
[tex]x = 1.67 + 1.06718737290547[/tex] [tex]x = 1.167 - 1.06718737290547[/tex]
[tex]x = 2.73718737290547[/tex] [tex]x = 0.60281262709453[/tex]
----------------------------------------------------------------------------------------------------------
6.[tex]10x^{2} - 10x + 9 = 5x^{2} + 4x + 1[/tex]
[tex]10x^{2} - 5x^{2} - 10x + 10x + 9 - 1 = 5x^{2} - 5x^{2} + 4x + 10x + 1 - 1[/tex]
[tex]5x^{2} + 8 = 14x[/tex]
[tex]5x^{2} - 14x + 8 = 14x - 14x[/tex]
[tex]5x^{2} - 14x + 8 = 0[/tex]
[tex]x = \frac{-(-14) + \sqrt{(-14)^{2} - 4(5)(8)}}{2(5)} [/tex]
[tex]x = \frac{14 +/- \sqrt{196 - 160}}{10} [/tex]
[tex]x = \frac{14 +/- \sqrt{36}}{10} [/tex].
[tex]x = \frac{14 +/- 6}{10} [/tex]
[tex]x = 1.4 +/- 0.6[/tex]
[tex]x = 1.4 + 0.6[/tex] [tex]x = 1.4 - 0.6[/tex]
[tex]x = 2[/tex] [tex]x = 0.8[/tex]
