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