Answer:
x = 3
[tex]x=-1\frac{1}{3}[/tex] or [tex]x=-\frac{4}{3}[/tex]
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
[tex]\frac{3x}{3} :-\frac{4}{3}[/tex]
[tex]x=-1\frac{1}{3}[/tex]
Method 2: Quadratic Formula
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
3x² - 5x - 12 = 0
a = 3
b = - 5
c = - 12
[tex]x=\frac{-(-5)±\sqrt{(-5)^{2} -4((3)(-12))} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±\sqrt{25 -4((3)(-12))} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±\sqrt{25 +144} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±\sqrt{169} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±13}{2(3)}[/tex]
[tex]x=\frac{5±13}{6}[/tex]
Two separate equations
One must have a + (positive) and the other will have a - (negative).
[tex]x=\frac{5+13}{6}[/tex]
[tex]x=\frac{18}{6}[/tex]
x = 18 ÷ 6
x = 3
[tex]x=\frac{5-13}{6}[/tex]
[tex]x=\frac{-8}{6}[/tex]
x = - 8 ÷ 6
[tex]x=-1\frac{1}{3}[/tex]
