Decide what values of the variable cannot possibly be solutions for the equation.
-$$( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5$$
A) $\left\{ \frac { 2 } { 7 } , - \frac { 4 } { 7 } \right\}$
B) $\left\{ - \frac { 8 } { 7 } , - \frac { 2 } { 7 } \right\}$
C) $\{ 5 , - 1 \}$
D) $\left\{ - \frac { 2 } { 7 } , \frac { 4 } { 7 } \right\}$

Question

Quizplus · Accepted Answer

The expression $-7x + 3$ must not equal zero, as it would make the equation undefined. Solving $-7x + 3 = 0$ gives $x = \frac{3}{7}$, which is not in any of the options. However, solving the quadratic equation may yield extraneous solutions, and checking each option shows that the values in option D do not satisfy the original equation.

Decide What Values of the Variable Cannot Possibly Be Solutions (−7x+3)2=4(−7x+3)+5( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5(−7x+3)2=4(−7x+3)+5

Decide What Values of the Variable Cannot Possibly Be Solutions $( - 7 x + 3 ) ^ { 2 } = 4 ( - 7 x + 3 ) + 5$