Question

If using the method of completing the square to solve the quadratic equation x^2-3x+20=0x 2 −3x+20=0, which number would have to be added to "complete the square"?

Answer 1

(x−21​)^2=81/4

Answer 2

The polynomial must be added by 2.25 on each side of the equation.

Explanation:

Let
`x^(2)-3\cdot x +20 = 0`, we need to add each side by 2.25 to complete the square, that is, expanding the polynomial so that factor of a perfect square trinomial can be done:

1)
`x^(2)-3\cdot x +20 = 0` Given

2)
`(x^(2)-3\cdot x +20) +2.25 = 2.25 + 0` Compatibility with addition/Commutative property

3)
`(x^(2)-3\cdot x +2.25) +20 = 2.25` Commutative, associative and modulative properties.

4)
`(x-1.5)^(2) +20 = 2.25` Perfect square trinomial/Result