Solve the equation. $( x + 1 ) ^ { 2 } = - 2 ( x + 1 ) - 1$
A) $x = - 2 , x = 2$
B) x=-2
C) x=2
D) x=0
E) x=-1

Question

Quizplus · Accepted Answer

Expanding $(x+1)^2$ gives us $x^2+2x+1$. Substituting this back into the original equation, we get the quadratic equation $x^2+4x+2=0$. Using the quadratic formula, we find that the solutions are $x=-2\pm \sqrt{2}$. However, only one of these solutions satisfies the original equation, which is $x=-2-\sqrt{2}$. Therefore, the answer is B) x=-2.

Solve the Equation (x+1)2=−2(x+1)−1( x + 1 ) ^ { 2 } = - 2 ( x + 1 ) - 1(x+1)2=−2(x+1)−1

Solve the Equation $( x + 1 ) ^ { 2 } = - 2 ( x + 1 ) - 1$