Question

Factor-
`x^2+10x+21=0`

Answer 1

x = 5 ± √46

Explanation:

`-x^2 + 10x + 21 = 0`

Take -1 common from L.H.S.

`=> -1(x^2 -10x - 21) = 0`

Take -1 to R.H.S.

`=> x^2 - 10x - 21 = 0`

Solve x using quadratic formula.

`=> x = (-(-10) + √(10^2 - 4 * (-21) * 1) )/(2 * 1) \: or \:(-(-10) - √(10^2 - 4 * (-21) * 1) )/(2 * 1)`

`=> x = (10 + √(100 + 84) )/(2) \: or \:(10 - √(100 + 84) )/(2)`

`=> x = (10 + √(184) )/(2) \: or \: (10-√(184) )/(2)`

`=> x = (10 + 2√(46) )/(2) \: or \: (10 - 2√(46) )/(2)`

`=> x = (5 + √(46) ) \: or \: (5 - √(46) )`