Question

Solve the equation by factoring. 3x^2-5x-12=0

Answer 1

Hope this helps you out! :)

Answer 2

Answer:

x = 3

$x=-1\frac{1}{3}$ or $x=-\frac{4}{3}$

Step-by-step explanation:

3x² - 5x - 12 = 0

Method 1: Factoring

3x² + 4x - 9x - 12 = 0

(3x² + 4x) + (- 9x - 12) = 0

x(3x + 4) - 3(3x + 4) = 0

(x - 3)(3x + 4) = 0

Two separate equations

x - 3 = 0

3x + 4 = 0

x - 3 = 0

x - 3 + 3 = 0 + 3

3x + 4 = 0

3x + 4 - 4 = 0 - 4

3x = - 4

$\frac{3x}{3} :-\frac{4}{3}$

$x=-1\frac{1}{3}$

Method 2: Quadratic Formula

Ignore the A before the ±, it wouldn't let me type it correctly.

$x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}$

3x² - 5x - 12 = 0

a = 3

b = - 5

c = - 12

$x=\frac{-(-5)±\sqrt{(-5)^{2} -4((3)(-12))} }{2(3)}$

$x=\frac{-(-5)±\sqrt{25 -4((3)(-12))} }{2(3)}$

$x=\frac{-(-5)±\sqrt{25 +144} }{2(3)}$

$x=\frac{-(-5)±\sqrt{169} }{2(3)}$

$x=\frac{-(-5)±13}{2(3)}$

$x=\frac{5±13}{6}$

Two separate equations

One must have a + (positive) and the other will have a - (negative).

$x=\frac{5+13}{6}$

$x=\frac{18}{6}$

x = 18 ÷ 6

x = 3

$x=\frac{5-13}{6}$

$x=\frac{-8}{6}$

x = - 8 ÷ 6

$x=-1\frac{1}{3}$