To solve the equation x² + 2x + 1 = 17, we first want to rearrange it into a standard quadratic form, which is ax² + bx + c = 0.
1. Start by subtracting 17 from both sides of the equation:
x² + 2x + 1 – 17 = 0
This simplifies to:
x² + 2x – 16 = 0
2. Now we can factor the quadratic equation if possible. We are looking for two numbers that multiply to -16 (the constant term) and add up to 2 (the coefficient of x).
After testing a few pairs, we find that 4 and -4 work:
(x + 4)(x – 4) = 0
3. Set each factor equal to zero:
x + 4 = 0 or x – 4 = 0
4. This gives us:
x = -4 or x = 4
Therefore, the solutions to the equation x² + 2x + 1 = 17 are:
x = -4 and x = 4.