Solve these equations algebraically. |π₯^2 β 4| = 4 β π₯
To solve this equation algebraically, we will separate it into two cases.
Case 1: π₯^2 - 4 = 4 - π₯
Rearranging the equation, we get:
π₯^2 + π₯ - 8 = 0
Factoring the quadratic equation, we have:
(π₯ + 4)(π₯ - 2) = 0
Setting each factor equal to zero, we get:
π₯ + 4 = 0 or π₯ - 2 = 0
π₯ = -4 or π₯ = 2
Case 2: π₯^2 - 4 = π₯ - 4
Simplifying the equation, we have:
π₯^2 - π₯ = 0
Factoring out π₯, we get:
π₯(π₯ - 1) = 0
Setting each factor equal to zero, we get:
π₯ = 0 or π₯ - 1 = 0
π₯ = 0 or π₯ = 1
Therefore, the solution to the equation |π₯^2 β 4| = 4 β π₯ is π₯ = -4, 0, 1, or 2.