Question

13. Solve each equation using the quadratic formula.

2
x + 4x 21 = 0


Please help me with 13!!!

Answer 1

`x = 3, \: x = - 7`

Explanation:

`using \: the \: quadratic \: formula \\ x = \frac{ - b± \sqrt{b {}^(2) - 4ac} }{2a}`

`compare \: with \: the \: general \: form \: of \: quadratic \: equation \\ ax {}^(2) + bx + c`

`a = 1, \: b = 4, \: c = - 21`

`substituting; \\ x = \: \frac{ - 4± \sqrt{4 {}^(2) - 4 * 1 * - 21 } }{2 * 1}`

`x = ( - 4 ± √(16 + 84) )/(2)`

`x = ( - 4± √(100) )/(2)`

`x = ( - 4±10)/(2)`

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

`x = (6)/(2) \: or \: x \: ( - 14)/(2)`

Therefore X = 3, X = -7