Question

The sum of all the real roots of the equation |x-2|^2+|x-2|-2=0

Answer 1

$(x - 2) ^{2} + (x - 2) - 2 =0 \\ x ^{2} + 4 - 4x + x - 2 - 2 = 0 \\ x ^{2} + 4 - 3x - 4 = 0 \\ x {}^{2} - 3x + 4 - 4 = 0 \\ x ^{2} - 3x + 0 = 0 \\ x {}^{2} - 3x = 0 \\ x \times x = 3 \times x \\ (x \times x) \div x = 3 \\ x = 3$