Solve the equation after making an appropriate substitution.
-$$3 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 0$$
A) $\left\{ - \frac { 4 } { 3 } , - 4 \right\}$
B) $\{ 0,3 \rangle$
C) $\left\{ - \frac { 1 } { 3 } , - 5 \right\}$
D) $\left\{ - \frac { 4 } { 3 } , - 5 \right\}$

Question

Quizplus · Accepted Answer

Let $ y = x + 1 $. The equation becomes $ 3y^2 + 13y + 4 = 0 $. Solving this quadratic equation gives $ y = -\frac{4}{3} $ and $ y = -1 $. Substituting back $ x = y - 1 $, we get $ x = -\frac{4}{3} - 1 = -\frac{7}{3} $ and $ x = -1 - 1 = -2 $. However, there seems to be a mistake in the options provided, as the correct solutions for $ x $ should be $ -\frac{4}{3} - 1 = -\frac{7}{3} $ and $ -1 - 1 = -2 $. The closest option is D, assuming a typographical error in the problem or options.

Solve the Equation After Making an Appropriate Substitution 3(x+1)2+13(x+1)+4=03 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 03(x+1)2+13(x+1)+4=0

Solve the Equation After Making an Appropriate Substitution $3 ( x + 1 ) ^ { 2 } + 13 ( x + 1 ) + 4 = 0$