How do you solve the modulus of a quadratic equation?

Below example will help you in understanding how we can solve the modulus of a quadratic equation.

|x2 – 6| = -x + 6

When |x2 – 6| ≥ 0

x2 – 6 = -x + 6

x2 + x – 12 = 0

x2 – 3x + 4x – 12 = 0

x(x – 3) + 4(x – 3) = 0

(x – 3)(x + 4) = 0

x = 3 or x = -4

When |x2 – 6| < 0

-(x2 – 6) = -x + 6

x2 – x = 0

x(x – 1) = –

x = 0 or x = 1

Hence, there are four solutions for the modulus quadratic equation, they are 0, 1, 2, -4.

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