To solve a quadratic equation by factoring:
$3x^2 = 5 - 14x$ | (original equation) |
$3x^2 + 14x - 5 = 0$ | (put in standard form: subtract $\,5\,$ from both sides; add $\,14x\,$ to both sides) |
$(3x-1)(x+5) = 0$ | (factor the left-hand side; you may want to use the factor by grouping method) |
$3x-1 = 0\ \ \text{ or }\ \ x + 5 = 0$ | (use the Zero Factor Law) |
$3x = 1\ \ \text{ or }\ \ x = -5$ | (solve the simpler equations) |
$\displaystyle x = \frac{1}{3}\ \ \text{ or }\ \ x = -5$ | (solve the simpler equations) |
$(2x+3)(5x-1) = 0$ | (original equation) |
$2x+3 = 0\ \ \text{ or }\ \ 5x - 1 = 0$ | (use the Zero Factor Law) |
$2x = -3\ \ \text{ or }\ \ 5x = 1$ | (solve the simpler equations) |
$\displaystyle x = -\frac{3}{2}\ \ \text{ or }\ \ x = \frac{1}{5}$ | (solve the simpler equations) |
$10x^2 - 11x - 6 = 0$ | (original equation) |
$(5x+2)(2x-3) = 0$ | (factor the left-hand side; you may want to use the factor by grouping method) |
$5x+2 = 0\ \ \text{ or }\ \ 2x - 3 = 0$ | (use the Zero Factor Law) |
$5x = -2\ \ \text{ or }\ \ 2x = 3$ | (solve the simpler equations) |
$\displaystyle x = -\frac{2}{5}\ \ \text{ or }\ \ x = \frac{3}{2}$ | (solve the simpler equations) |
CONCEPT QUESTIONS EXERCISE:
For more advanced students, a graph is displayed. |
PROBLEM TYPES:
IN PROGRESS |