Solve the equation by making an appropriate substitution.
-$$( x - 5 ) ^ { 2 } + 2 ( x - 5 ) - 8 = 0$$
A) $\{ 1,7 \}$
B) $\{ - 9 , - 3 \}$
C) $\{ 3,9 \}$
D) $\{ - 7 , - 1 \}$

Question

Quizplus · Accepted Answer

Let $u = x - 5$, then the equation becomes $u^2 + 2u - 8 = 0$. Factoring or using the quadratic formula gives $u = 2$ or $u = -4$. Substituting back $u = x - 5$, we get $x = 7$ or $x = 1$.

Solve the Equation by Making an Appropriate Substitution (x−5)2+2(x−5)−8=0( x - 5 ) ^ { 2 } + 2 ( x - 5 ) - 8 = 0(x−5)2+2(x−5)−8=0

Solve the Equation by Making an Appropriate Substitution $( x - 5 ) ^ { 2 } + 2 ( x - 5 ) - 8 = 0$