Question

To complete the square and solve the equation m² - 16m = -59, f

Answer 1

To solve the equation m² - 16m = -59 by completing the square, follow the steps: 1) Move the constant term to the right side, 2) Group the variable terms, 3) Complete the square, 4) Isolate the squared term, 5) Take the square root, and 6) Solve for m.

Step-by-step explanation:

To complete the square and solve the equation m² - 16m = -59, we can follow these steps:

1. Move the constant term to the right side of the equation: m² - 16m - (-59) = 0
2. Group the variable terms: (m² - 16m) + 59 = 0
3. Complete the square by halving the coefficient of the linear term (-16) and squaring it: (m - 8)² + 59 = 64
4. Isolate the squared term: (m - 8)² = 64 - 59
5. Take the square root of both sides: m - 8 = ±√5
6. Solve for m by adding 8 to both sides: m = 8 ± √5

Therefore, the solutions to the equation are m = 8 + √5 and m = 8 - √5.