I was given this answers to a problems I solved but I do not understand what she means hope you can help.

Before attempting to solve this quadratic equation, determine how many solutions there will be for this quadratic equation. Explain your reasoning. Finally, solve the equation.
(x - 9)2 = 81

I too, came up with the same answer and agree that this is a positive number and we should expect there to be two solutions to this problem. Carrying out the square is exactly the same as using the quadratic formula it is where you substitute a, b and c into the formula. It gives you the same answer to the polynomial used. This is because the quadratic formula came from finishing the square. Completing the square method is like the father of the quadratic formula.

(x - 9)2 = 81
(x - 9) = �ã81
x = 9�}9
x = 18 or x = 0

This answer was inreponce to another student who came up with the same as i did.

Hi Charly,

Yes, your answer is correct. Nice work. However, the method you used is not completing the square. Which one might it be, do you think?

For you information, online "^" indicates an exponent, e.g., x^2 = x squared.

(x - 9)^2 = 81

x^2 -18x + 81 = 81

x^2 - 18x = 0

x(x-18) = 0

X = 18 or 0

Monash University - one of the top universities in Australia

Based on the response provided, it seems like the method used to solve the quadratic equation is not completing the square but rather using the square root property. The square root property is a method used to solve quadratic equations in the form of (x - a)² = b. In this case, the equation is (x - 9)² = 81, which can be rewritten as (x - 9) = √81.

To solve this equation using the square root property, we take the square root of both sides to isolate x:
√(x - 9) = ±√81

Simplifying further, we get:
x - 9 = ±9

Adding 9 to both sides of the equation gives us two possible solutions:
x = 9 + 9 = 18
x = 9 - 9 = 0

Therefore, the equation has two solutions: x = 0 and x = 18.

To complete the square, we would go through a different method, where we manipulate the equation to the form (x - h)² = k. But in this case, using the square root property was a suitable approach.