Finite Math Examples

$x^{2} - 3 x = x (x - 3)$

Step 1

Simplify $x (x - 3)$ .

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Step 1.1

Apply the distributive property.

$x^{2} - 3 x = x \cdot x + x \cdot - 3$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $x$ by $x$ .

$x^{2} - 3 x = x^{2} + x \cdot - 3$

Step 1.2.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 x = x^{2} - 3 x$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 50, - 49.9, - 49.8, - 49.7, - 49.6, - 48.7, - 48.5, - 48.4, - 48.3, - 47.9, - 47.8, - 47.6, - 47.5, - 47.4, - 47.2, - 47.1, - 46.9, - 46.8, - 46.3\overline{9}, - 46.1\overline{9}, - 45.7\overline{9}, - 45.6\overline{9}, - 45.3\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 45, - 44.8\overline{9}, - 44.6\overline{9}, - 44.4\overline{9}, - 43.6\overline{9}, - 43.5\overline{9}, - 43.4\overline{9}, - 43.2\overline{9}, - 43.1\overline{9}, - 43.0\overline{9}, - 42.8\overline{9}, - 42.5\overline{9}, - 42.3\overline{9}, - 42.2\overline{9}, - 42.1\overline{9}, - 42.0\overline{9}, - 42, - 41.8\overline{9}, - 41.5\overline{9}, - 41.4\overline{9}, - 41.3\overline{9}, - 41.2\overline{9}, - 40.6\overline{9}, - 40.5\overline{9}, - 40.2\overline{9}, - 40.0\overline{9}, - 40, - 39.8\overline{9}, - 39.6\overline{9}, - 39.5\overline{9}, - 39.3\overline{9}, - 39.1\overline{9}, - 38.7\overline{9}, - 38.6\overline{9}, - 38.3\overline{9}, - 38.2\overline{9}, - 38, - 37.8\overline{9}, - 37.5\overline{9}, - 37.4\overline{9}, - 37.3\overline{9}, - 37.2\overline{9}, - 37.0\overline{9}, - 36.8\overline{9}, - 36.6\overline{9}, - 36.5\overline{9}, - 36.1\overline{9}, - 36.0\overline{9}, - 35, - 34.8\overline{9}, - 34.7\overline{9}, - 34.6\overline{9}, - 34.5\overline{9}, - 34.2\overline{9}, - 34.1\overline{9}, - 34.0\overline{9}, - 34, - 33.8\overline{9}, - 33.7\overline{9}, - 33.4\overline{9}, - 33.2\overline{9}, - 33, - 32.8\overline{9}, - 32.6\overline{9}, - 32.5\overline{9}, - 32.3\overline{9}, - 32.2\overline{9}, - 31.8\overline{9}, - 31.7\overline{9}, - 31.4\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 31.1\overline{9}, - 30.8\overline{9}, - 30.7\overline{9}, - 30.6\overline{9}, - 30.4\overline{9}, - 30.3\overline{9}, - 30.2\overline{9}, - 30.1\overline{9}, - 30, - 29.8\overline{9}, - 29.7\overline{9}, - 29.0\overline{9}, - 29, - 28.3\overline{9}, - 28.2\overline{9}, - 27.5\overline{9}, - 27.4\overline{9}, - 27.3\overline{9}, - 26.8\overline{9}, - 26.7\overline{9}, - 26.6\overline{9}, - 26.5\overline{9}, - 26.4\overline{9}, - 26.1\overline{9}, - 25.8\overline{9}, - 25.7\overline{9}, - 25.5\overline{9}, - 25.0\overline{9}, - 25, - 24.8\overline{9}, - 24.7\overline{9}, - 24.6\overline{9}, - 24.5\overline{9}, - 24.2\overline{9}, - 24, - 23, - 22.8\overline{9}, - 22.5\overline{9}, - 22.4\overline{9}, - 21.3\overline{9}, - 21.2\overline{9}, - 21.1\overline{9}, - 21.0\overline{9}, - 20.8\overline{9}, - 20.7\overline{9}, - 20.4\overline{9}, - 20, - 19.5\overline{9}, - 19.0\overline{9}, - 18.7\overline{9}, - 18.6\overline{9}, - 18.5\overline{9}, - 18.3\overline{9}, - 18.1\overline{9}, - \frac{35}{2}, - 17.2\overline{9}, - 17, - 16.8\overline{9}, - 16.6\overline{9}, - 16.5\overline{9}, - \frac{33}{2}, - 16.2\overline{9}, - 16, - 15.8\overline{9}, - 15.7\overline{9}, - 15.6\overline{9}, - 15.5\overline{9}, - \frac{31}{2}, - 14.8\overline{9}, - 14.5\overline{9}, - 14.3\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 14, - 13.8\overline{9}, - 13.7\overline{9}, - 13.6\overline{9}, - \frac{27}{2}, - 13.1\overline{9}, - 13, - 12.8\overline{9}, - 12.6\overline{9}, - 12.5\overline{9}, - 12.2\overline{9}, - 12.1\overline{9}, - 11.8\overline{9}, - \frac{59}{5}, - \frac{57}{5}, - 11.2\overline{9}, - \frac{56}{5}, - 11.0\overline{9}, - \frac{52}{5}, - 10.2\overline{9}, - \frac{51}{5}, - 9.9, - \frac{49}{5}, - \frac{19}{2}, - \frac{47}{5}, - 9, - 8.9, - \frac{44}{5}, - 8.7, - \frac{43}{5}, - 8.3, - \frac{41}{5}, - \frac{39}{5}, - 7.7, - \frac{38}{5}, - \frac{15}{2}, - \frac{36}{5}, - \frac{34}{5}, - 6.7, - \frac{33}{5}, - \frac{13}{2}, - 5.9, - \frac{29}{5}, - 5.1, - 5, - 4.9, - \frac{24}{5}, - 4.7, - \frac{23}{5}, - \frac{21}{5}, - 4.1, - 4, - 3.9, - \frac{18}{5}, - \frac{7}{2}, - \frac{17}{5}, - \frac{16}{5}, - 3, - 2.9, - \frac{13}{5}, - \frac{12}{5}, - 2.3, - \frac{11}{5}, - 2, - 1.9, - \frac{9}{5}, - \frac{8}{5}, - \frac{3}{2}, - \frac{7}{5}, - \frac{6}{5}, - 0.9, - \frac{4}{5}, - 0.7, - \frac{3}{5}, - \frac{1}{2}, - \frac{2}{5}, - 0.3, - 0.1, 0.1, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}, 0.9, 1, 1.1, 1.3, \frac{7}{5}, \frac{3}{2}, \frac{8}{5}, 1.7, \frac{9}{5}, 1.9, 2, 2.1, 2.3, \frac{12}{5}, \frac{5}{2}, \frac{13}{5}, 2.7, \frac{14}{5}, 2.9, 3, 3.1, \frac{16}{5}, \frac{7}{2}, 3.7, \frac{19}{5}, 4, 4.1, \frac{21}{5}, 4.3, \frac{9}{2}, \frac{23}{5}, \frac{24}{5}, 5.1, \frac{26}{5}, 5.3, \frac{27}{5}, \frac{11}{2}, \frac{28}{5}, 5.7, \frac{29}{5}, 5.9, 6, \frac{31}{5}, \frac{13}{2}, \frac{33}{5}, 6.7, \frac{34}{5}, 6.9, 7.1, \frac{36}{5}, 7.3, \frac{15}{2}, 7.7, 8, 8.1, \frac{41}{5}, \frac{42}{5}, \frac{17}{2}, \frac{43}{5}, 8.7, 8.9, 9.1, \frac{46}{5}, 9.3, \frac{48}{5}, 9.7, 10.1, 10.3, \frac{52}{5}, \frac{53}{5}, 11, 11.1, \frac{23}{2}, \frac{58}{5}, 11.7, \frac{59}{5}, 11.9, 12.1, 12.2, 12.3, \frac{62}{5}, \frac{25}{2}, 12.6, 12.8, 13.1, 13.3, 13.4, \frac{27}{2}, 13.7, 13.8, 14, 14.1, 14.3, 14.4, \frac{29}{2}, 15, 15.1, \frac{31}{2}, 15.7, 15.8, 15.9, 16, 16.1, 16.2, 16.3, 16.4, \frac{33}{2}, 16.6, 16.7, 16.8, 16.9, 17.6, 17.7, 17.9, 18.2, 18.4, 18.5, 18.6, 18.7, 18.8, 18.9, 19.2, 19.8, 19.9, 20.5, 20.6, 20.7, 20.9, 21.3, 21.4, 21.5, 22.2, 22.3, 22.4, 22.5, 22.9, 23.3, 23.4, 23.5, 23.6, 23.7, 23.8, 23.9, 24, 24.1, 24.3, 24.4, 25, 25.1, 25.3, 25.4, 25.5, 25.7, 25.8, 25.9, 26, 26.1, 27.1, 27.2, 27.4, 27.5, 27.9, 28, 28.1, 28.2, 28.9, 29, 29.2, 29.3, 29.4, 29.5, 29.8, 29.9, 30.4, 30.5, 30.8, 31, 31.3, 31.4, 31.5, 31.7, 31.8, 31.9, 32.1, 32.2, 32.4, 32.5, 32.6, 32.7, 33, 33.1, 33.3, 33.4, 33.5, 33.6, 33.7, 34, 34.1, 34.4, 34.5, 34.7, 34.9, 35.2, 35.3, 35.4, 35.5, 35.7, 35.8, 35.9, 36.2, 36.3, 36.5, 36.7, 36.8, 36.9, 37, 37.2, 37.3, 37.5, 37.6, 37.7, 37.8, 38, 38.1, 38.4, 38.6, 39.4, 39.5, 39.6, 39.9, 40, 40.2, 40.4, 40.5, 41.6, 41.7, 42.2, 42.3, 42.5, 42.7, 43, 43.1, 43.2, 43.4, 43.6, 43.9, 44, 44.1, 44.2, 44.4, 44.5, 44.7, 44.8, 44.9, 45, 45.3, 45.4, 45.5, 45.6, 45.9, 46, 46.1, 46.2, 46.3, 46.4, 46.5, 46.6, 46.8, 47.2, 47.3, 47.4, 47.5, 48.5, 48.6, 48.7, 48.8, 49.1, 49.2, 49.4, 49.5, 49.6, 49.8, 49.9$

Step 3