Question

By Factoring And Using Quadratic Formula x raise to two minus 10x is equals to negative 21

Answer 1

`x =3` or
`x = 7`

Explanation:

Given

`x^2 - 10x = -21`

Required

Solve by factoring & quadratic formula

By Factoring:

`x^2 - 10x = -21`

Equate to 0

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

Expand:

`x^2 - 7x -3x+21 = 0`

Factorize:

`x(x-7)-3(x-7) = 0`

`(x-3)(x-7) = 0`

`x -3 = 0` or
`x - 7 = 0`

`x =3` or
`x = 7`

By quadratic

`x^2 - 10x = -21`

Equate to 0

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

For

`ax^2 + bx + c = 0`

x is solved using:

`x = (-b\±√(b^2-4ac))/(2a)`

where

`a = 1`;
`b = -10`;
`c = 21`

So:

`x = (-(-10)\±√((-10)^2-4*1*21))/(2*1)`

`x = (10\±√(100-84))/(2)`

`x = (10\±√(16))/(2)`

`x = (10\±4)/(2)`

Split

`x = (10+4)/(2)` or
`x = (10-4)/(2)`

`x = (14)/(2)` or
`x = (6)/(2)`

`x = 7` or
`x =3`