Solve for x |x^2+x-1|=1

Problem

|x2+x−1|=1

Solution

1. Apply the definition of absolute value to split the equation into two separate cases where the expression inside the absolute value equals 1 or −1

x2+x−1=1

x2+x−1=−1

2. Solve the first case by setting the quadratic equation to zero.

x2+x−2=0

3. Factor the quadratic in the first case.

(x+2)*(x−1)=0

4. Identify the roots for the first case.

x=−2

x=1

5. Solve the second case by setting the quadratic equation to zero.

x2+x=0

6. Factor the quadratic in the second case by taking out the greatest common factor.

x*(x+1)=0

7. Identify the roots for the second case.

x=0

x=−1

Final Answer

x={−2,−1,0,1}

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