Solve for x fifth root of x^2+2x=-1

Problem

√(5,x2+2*x)=−1

Solution

1. Raise both sides to the fifth power to eliminate the radical.

(√(5,x2+2*x))5=(−1)5

2. Simplify both sides of the equation.

x2+2*x=−1

3. Add 1 to both sides to set the quadratic equation to zero.

x2+2*x+1=0

4. Factor the quadratic expression, which is a perfect square trinomial.

(x+1)2=0

5. Solve for x by taking the square root of both sides and isolating the variable.

x+1=0

x=−1

Final Answer

√(5,x2+2*x)=−1⇒x=−1

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