To solve the equation x² – 18x + 81 = 25, we first need to rearrange it into standard form. This involves moving all terms to one side of the equation.
1. Start by subtracting 25 from both sides:
x² – 18x + 81 – 25 = 0
This simplifies to:
x² – 18x + 56 = 0
2. Next, we can factor this quadratic equation. We’re looking for two numbers that multiply to +56 and add up to -18. The numbers -14 and -4 fit these conditions.
3. So we can factor the equation as:
(x – 14)(x – 4) = 0
4. Now, we can set each factor equal to zero:
x – 14 = 0 or x – 4 = 0
This gives us:
x = 14 or x = 4
5. Therefore, the solutions to the equation x² – 18x + 81 = 25 are:
x = 14 and x = 4