The square of Faizal's age, in years, is 12 more than his father's age. One year ago, Faizal's age was \( \frac{1}{6} \) of his father's age. Find Faizal's present age.

Let's denote Faizal's current age as \( F \) and his father's current age as \( P \). From the problem, we have two equations to work with: 1. The square of Faizal's age is 12 more than his father's age: \[ F^2 = P + 12 \] 2. One year ago, Faizal’s age was \( \frac{1}{6} \) of his father’s age at that time: \[ F - 1 = \frac{1}{6}(P - 1) \] Now, we can manipulate these equations to find Faizal’s current age. From the second equation, we multiply both sides by 6 to eliminate the fraction: \[ 6(F - 1) = P - 1 \] This simplifies to: \[ 6F - 6 = P - 1 \quad \Rightarrow \quad P = 6F - 5 \] Next, we substitute \( P \) in the first equation: \[ F^2 = (6F - 5) + 12 \] This simplifies to: \[ F^2 = 6F + 7 \] Rearranging gives us a quadratic equation: \[ F^2 - 6F - 7 = 0 \] Now we can solve for \( F \) using the quadratic formula: \[ F = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{6 \pm \sqrt{(-6)^2 - 4 \cdot 1 \cdot (-7)}}{2 \cdot 1} \] Calculating the discriminant: \[ = \frac{6 \pm \sqrt{36 + 28}}{2} = \frac{6 \pm \sqrt{64}}{2} = \frac{6 \pm 8}{2} \] Now we have two potential solutions for \( F \): 1. \( F = \frac{14}{2} = 7 \) 2. \( F = \frac{-2}{2} = -1 \) (not valid, since age can't be negative) Thus, Faizal's present age is: \[ \boxed{7} \text{ years old.} \]