Question

If using the method of completing the square to solve the quadratic equation x2 – 3x + 20 = 0, which number would have to be added to "complete the square"?​

Answer 1

⁹/₄

Explanation:

The square is: a²-2ab+b²

We have

`x^2-3x`

it's:
`x^2-2\cdot x\cdot\frac32`

so we need:
`\left(\frac32\right)^2=\frac94`

`x^2-2\cdot x\cdot\frac32+\frac94-\frac94+20=0\\\\(x-\frac32)^2-2.25+20=0\\\\(x-\frac32)^2=-17.75`

witch, of course, means no solution