How do you solve $3 x^{2} + 20 x + 36 = 4$ $3x^2 + 20x + 36 = 4$ by completing the square?

Question

2208 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-18T18:15:02

$f (x) = 3 x^{2} + 20 x + 32$ $f(x) = 3x^2 + 20x + 32$ = $3 (x^{2} + \frac{20 x}{3} + \frac{32}{3}) = 0$ $3(x^2 + (20x)/3 + 32/3) = 0$

$x^{2} + \frac{20 x}{3} + \frac{100}{9} - \frac{100}{9} + \frac{32}{3} = 0$ $x^2 + (20x)/3 + 100/9 - 100/9 + 32/3 = 0$

$= {(x + \frac{10}{3})}^{2} - \frac{4}{9} = 0$ $= (x + 10/3)^2 - 4/9 = 0$ -> $(x + \frac{10}{3}) = \pm \frac{2}{3}$ $(x + 10/3) = +- 2/3$

$(x + \frac{10}{3}) = \frac{2}{3} \to x = - \frac{10}{3} + \frac{2}{3} = - \frac{8}{3}$ $(x + 10/3) = 2/3 -> x = -10/3 + 2/3 = -8/3$

$(x + \frac{10}{3}) = - \frac{2}{3} \to x = - \frac{10}{3} - \frac{2}{3} = - 12 / 3 = - 4$ $(x + 10/3) = -2/3 -> x = -10/3 - 2/3 = -12//3 = -4$

How do you solve 3x2+20x+36=43x^2 + 20x + 36 = 4 by completing the square?