deduce the completed square form for the following 2x^2+16x-10
and your thinking is ...? I will be happy to critique your thinking.
Try writing it as
2(x^2 + 8x + __) -10 first, and then worry about what to add in the ___ slot to complete the square, and subtract from the constant at the end.
To deduce the completed square form for the quadratic equation 2x^2+16x-10, we need to follow a few steps:
Step 1: Make sure the coefficient of the x^2 term is 1. In the given equation, the coefficient is already 2, so we divide the entire equation by 2 to get: x^2 + 8x - 5.
Step 2: Take half of the coefficient of the x term and square it. Half of 8 is 4, and 4 squared is 16. Add this value as a constant to the equation. The equation becomes: x^2 + 8x + 16 - 5.
Step 3: Rearrange the equation, grouping the terms: (x^2 + 8x + 16) - 5.
Step 4: Rewrite the grouped terms as a perfect square and simplify: (x + 4)^2 - 5.
So, the completed square form for the equation 2x^2+16x-10 is (x + 4)^2 - 5.