Question

Janaina is trying to solve the following equation by completing the square: x^2+18x-9 = 0.She successfully rewrites the above equation in the following form: (x + b)^2 = c,where b and c are integers. What is the value of c?

Answer 1

After completing the square for the equation x^2 + 18x - 9 = 0, the value of 'c' in the form (x + b)^2 = c is found to be 72.

Step-by-step explanation:

Janaina is working on completing the square for the quadratic equation x^2 + 18x - 9 = 0. To rewrite this equation in the form (x + b)^2 = c, where b and c are integers, she needs to complete the square. This involves adding and subtracting the square of half the coefficient of x (which is 9 in this case) inside the equation. After adding 81 to both sides of the equation to complete the square, the equation becomes (x + 9)^2 = 81 - 9, which simplifies to (x + 9)^2 = 72. Therefore, the value of c is 72.

Answer 2

The Answer Is :
c = x^2 + 2bx + b^2