Question

If using the method of completing the square to solve the quadratic equation x^2 -4x +10 =0, which number would have to be added to complete the square?

Answer 1

Answer:

4 would have to be added to complete the square.

Step-by-step explanation:

We are given the following quadratic equation the question:

$x^2 -4x +10 =0$

We have to form a whole square to solve the quadratic equation.

$x^2 + ax + b\\=(x+c)^2+d\\\text{where}\\\\c = \dfrac{a}{2}$

We add and subtract the square of the coefficient of x.

$x^2 -4x =-10\\x^2 -4x + 4=-10+4\\(x-2)^2=-6\\x-2 =\pm \sqrt{6}i\\x = 2+\sqrt6i , 2-\sqrt6i$

Thus, we added and subtracted 4 in the quadratic equation to make it a complete square.