Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
-$$( 3 x - 7 ) ^ { 2 } - 4 ( 3 x - 7 ) - 12 = 0$$
A) $\left\{ \frac { 13 } { 3 } , \frac { 5 } { 3 } \right\}$
B) $\left\{ - \frac { 13 } { 3 } , - \frac { 5 } { 3 } \right\}$
C) $\left\{ \frac { 1 } { 3 } , - \frac { 9 } { 3 } \right\}$
D) $\left\{ - \frac { 1 } { 7 } , \frac { 9 } { 3 } \right\}$

Question

Quizplus · Accepted Answer

Let $u = 3x - 7$. The equation becomes $u^2 - 4u - 12 = 0$. Solving this quadratic equation for $u$ and then substituting back to find $x$ yields the solutions $\frac{13}{3}$ and $\frac{5}{3}$.

Solve Equations That Are Quadratic in Form Solve the Equation (3x−7)2−4(3x−7)−12=0( 3 x - 7 ) ^ { 2 } - 4 ( 3 x - 7 ) - 12 = 0(3x−7)2−4(3x−7)−12=0

Solve Equations That Are Quadratic in Form
Solve the Equation $( 3 x - 7 ) ^ { 2 } - 4 ( 3 x - 7 ) - 12 = 0$