Question

If using the method of completing the square to solve the quadratic equation x²-19x+35=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square for the equation x²-19x+35=0, first move the constant term to the other side. Then, calculate (b/2)² with b as -19, resulting in 361/4. Add and subtract this number to create a perfect square trinomial.

Step-by-step explanation:

To complete the square for the quadratic equation x²-19x+35=0, you must first ensure the equation is in the form x²+bx+c=0. When completing the square, you focus on the x² and bx terms; specifically, you want to transform the x²+bx part into a perfect square trinomial. A perfect square trinomial is of the form (x+d)², which expands to x² + 2dx + d². The d here is the number you would need to find. To obtain it, you take b/2 and square it. In your case, b is -19, so b/2 is -19/2. Squaring this gets you (-19/2)², which equals 361/4. That's the number you'd add to both sides to complete the square.