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If using the method of completing the square to solve the quadratic equation x, squared, minus, 19, x, plus, 35, equals, 0x
2
−19x+35=0, which number would have to be added to "complete the square"?
Answer
Attempt 1 out of 5

Answer 1

To complete the square for the quadratic equation \( x^2 - 19x + 35 = 0 \), we need to focus on the \( x^2 - 19x \) part of the equation.

To complete the square:

1. Take the coefficient of \( x \), which is \(-19\).
2. Divide it by 2:
\[
-\frac{19}{2} = -9.5
\]
3. Square that result:
\[
(-9.5)^2 = 90.25
\]

So, to complete the square, you would need to add \( 90.25 \) to both sides of the equation.

Therefore, the number that needs to be added to complete the square is **90.25**.