Question

Resolva com fatoração:
6x^2+ 13x+6=0

Answer 1

$\\ 6x^2+13x+6 = 0 \\ \\ 6(x^2+ \frac{13x}{6} +1) = 0 \\ \\ x^2+ \frac{13x}{6} +1 = 0 \\ \\ x^2+ \frac{13x}{6} +1^2=0 \\ \\ x^2+ \frac{13x}{6}+ (\frac{13}{12})^2-(\frac{13}{12})^2+1=0 \\ \\ x^2+ \frac{13x}{6}+ (\frac{13}{12})^2 = (\frac{13}{12})^2-1 \\ \\ (x+ \frac{13}{12})^2 = \frac{169}{144} -1 \\ \\ (x+ \frac{13}{12})^2 = \frac{169}{144} -\frac{144}{144} \\ \\ (x+ \frac{13}{12})^2 = \frac{169-144}{144} \\ \\ (x+ \frac{13}{12})^2 = \frac{25}{144}$

$\\ \sqrt{ (x+ \frac{13}{12})^2} = \sqrt{ \frac{25}{144}} \\ \\ |x+\frac{13}{12}| = \frac{5}{12} \\ \\ x' = \frac{5}{12} - \frac{13}{12} \\ \\ x' = -\frac{8}{12} =\ \textgreater \ - \frac{2}{3} \\ ---------- \\ x" = -\frac{5}{12} - \frac{13}{12} \\ \\ x'' = -\frac{18}{12} =\ \textgreater \ -\frac{9}{6} = - \frac{3}{2}$

Answer 2

6x² + 13x + 6 = 0

A= 6

B= 13

C= 6

∆= b² - 4ac

∆= 13² - 4 • 6 • 6

∆= 169 - 144

∆= 25

x= - b ± √∆ / 2a

x= - 13± √25/2 • 6

x= - 13 ± 5 /12

x'= - 13 - 5/12 = -18/12 (÷6) =- 3/2

x''= - 13 + 5/12 =- 8/12 (÷4) =- 2/3

S= (- 2/3 ; - 3/2)