Write the equation 𝑦=𝑥2−20𝑥+103 in completed square form.

To write the equation y = x^2 - 20x + 103 in completed square form, we need to complete the square for the quadratic part of the equation, which is x^2 - 20x.

Step 1: Identify the coefficient of x, which is -20 in this case.

Step 2: Divide the coefficient by 2 and square the result. This is (-20/2)^2 = 100.

Step 3: Rewrite the equation, adding and subtracting the value calculated in step 2. This gives us y = (x^2 - 20x + 100) - 100 + 103.

Step 4: The expression in the parentheses is a perfect square, and it can be written as (x - 10)^2. So, the equation becomes y = (x - 10)^2 - 100 + 103.

Step 5: Simplify the equation to get the final completed square form. The equation becomes y = (x - 10)^2 + 3.

So, the completed square form of the equation y = x^2 - 20x + 103 is y = (x - 10)^2 + 3.