quadratic formula

Question

Find the exact solutions to the quadratic equations....

 

X²+6x-27=0           and          3x²=39

 

 

Please help...thank you

Answer 1

use quadratic formula   -6+or-√(36+4*1*27) = (-6 ± √144)/2 = (-6±12)/2 = -9,+3

 

 

 

3X^{2= 39}    X^{2=13   x=±}√13

 

move the -27 to the other  side of the problem

now we have X² + 6 x = 27

Complete the square on the left side   6/2=3^{2 = 9}

 

add 9 to both sides of the problem

 

X² + 6x +9 = 27 + 9 = 36

 

 

(X + 3 )^{2  = 36}

 

Take the square root of both sides

 

X+3 = ± 6

 

X= -3-6 = -9   and  -3+6 = +3