If using the method of completing the square to solve the quadratic equation x, squared, minus, 16, x, plus, 37, equals, 0x 2 −16x+37=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square for the quadratic equation \( x^2 - 16x + 37 = 0 \), we focus on the quadratic and linear terms, which are \( x^2 - 16x \).

To complete the square, we take the coefficient of \( x \), which is \(-16\), divide it by 2, and then square the result.

1. Divide \(-16\) by 2: \[ -16 \div 2 = -8 \]

2. Square \(-8\): \[ (-8)^2 = 64 \]

Thus, the number that needs to be added to complete the square is \( 64 \).

Now, if we rewrite the original equation with this in mind: \[ x^2 - 16x + 64 - 64 + 37 = 0 \] This can be simplified to: \[ (x - 8)^2 - 27 = 0 \]

So, the final answer is that we would add \( 64 \) to complete the square.