Question

Using the method of completing the square to solve the quadratic equation ::

x^2-20x+24=0
which number would have to be added to "complete the square"?

Answer 1

100 should be added to 'complete the squre'

Explanation:

`{x}^(2) - 20x + 24 = 0 \\ ( {x}^(2) + 2 * 10 * x + {10}^(2)) - {10}^(2) + 64 = 0 \\ {(x - 10)}^(2) - 100 + 64 = 0 \\ {( x - 10)}^(2) - 36 = 0 \\ {(x - 10)}^(2) = 36 \\ (x - 10) = \pm 6 \\ x = 10 \pm 6 \\ x = 10 + 6 \: \: or \: \: x = 10 - 6 \\ x = 16 \: \: or \: \: x = 4`