Solve Equations That Are Quadratic in Form
Solve the equation by making an appropriate substitution.
-$$( x - 5 ) ^ { 2 } - 2 ( x - 5 ) - 15 = 0$$
A) $\{ 2,10 \}$
B) $\{ - 8,0 \}$
C) $\{ 0,8 \}$
D) $\{ - 10 , - 2 \}$

Question

Quizplus · Accepted Answer

By substituting $u = x - 5$, the equation becomes a quadratic equation $u^2 - 2u - 15 = 0$, which factors to $(u - 5)(u + 3) = 0$. Solving for $u$ gives $u = 5$ and $u = -3$. Substituting back $x - 5 = u$, we find $x = 10$ and $x = 2$, hence the solution set is $\{2, 10\}$.

Solve Equations That Are Quadratic in Form Solve the Equation (x−5)2−2(x−5)−15=0( x - 5 ) ^ { 2 } - 2 ( x - 5 ) - 15 = 0(x−5)2−2(x−5)−15=0

Solve Equations That Are Quadratic in Form
Solve the Equation $( x - 5 ) ^ { 2 } - 2 ( x - 5 ) - 15 = 0$