Final answer:
To complete the square for the quadratic expression 2x^2 - 16x + 3, factor out the 2 and then use the number -8, which is half of the x coefficient -16, to form a perfect square trinomial. You'll add and subtract (8^2), then factor and simplify to obtain the final expression: 2(x - 8)^2 - 125.
Step-by-step explanation:
To complete the square for the expression 2x^2 - 16x + 3, first divide the entire expression by the coefficient of the x^2 term, which is 2, to simplify the process. You should then rewrite the expression in the form of (x - h)^2 by finding the value that makes -16x a complete square.
Divide the -16 by 2, which is the coefficient of x^2, to obtain -8. Now square the -8 to get 64, this is the number you'll add and subtract inside the parenthesis to create a perfect square.
Your expression will now look like this: 2(x^2 - 8x + 64 - 64) + 3. Factor the first three terms to get 2((x - 8)^2) and distribute the 2 across -64 to get -128. Finally, add the outside term, + 3, to get the expression in the completed square form: 2(x - 8)^2 - 125.