To solve the equation x² – 16x + 60 = 12, we first need to rewrite it in standard form. This means we will set the equation to zero.
1. **Rearranging the equation**: Subtract 12 from both sides:
x² – 16x + 60 – 12 = 0
This simplifies to:
x² – 16x + 48 = 0
2. **Factoring the quadratic**: We need to find two numbers that multiply to 48 and add up to -16. The numbers -12 and -4 fit these requirements.
Therefore, we can factor the quadratic as:
(x – 12)(x – 4) = 0
3. **Finding the roots**: Now, we set each factor equal to zero:
x – 12 = 0 or x – 4 = 0
From this, we find:
x = 12 or x = 4
4. **Conclusion**: The solutions to the equation x² – 16x + 60 = 12 are x = 12 and x = 4.