solve the given quadratic equations by using the quadratic formula

Question

x^2-8x+20=0                              and                            4x^2-4x+17=0

Answer 1

 ax2+bx+c = 0, Quadratic formula:  x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

 

 

1.   x^2-8x+20=0

a=1, b=-8 , c=20  Plug in the value for a, b and c in the quadratic formula

 

 

x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

x = [ -(-8) ± sqrt( (-8)^2 - 4(1)(20) ] / 2(1)      Simplify

 

x = [ 8 ± sqrt( 64 - 80) ] / 2

x = [ 8 ± sqrt( -16) ] / 2                ( no real solution if you have not learn imaginary solution )

 

(if you have learn imaginary solution then continue.....finding sqrt(-16) = 4i

 

x = [ 8 ± 4i ] / 2                Simplify by finding Greatest Common Factor GCF 

x = 2 (4 ± 2i ) / 2              cancel out 2 top and bottom

 

x =  4 ± 2i   Solutions: x = 4 + 2i & x = 4 - 2i  

 

 

 

2.     4x^2-4x+17=0

a=4, b= - 4 , c=17                Plug in the value for a, b and c in the quadratic formula

x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

x = [ -(-4) ± sqrt( (-4)^2 - 4(4)(17) ] / 2(4)      Simplify
x = [ 4 ± sqrt( 16 - 272) ] / 8
x = [ 4 ± sqrt( -256) ] / 8               ( no real solution if you have not learn imaginary solution )

(if you have learn imaginary solution then continue.....finding sqrt(-256) = 16i

x = [ 4 ± 16i ] / 8                Simplify by finding Greatest Common Factor GCF
x = 4 ( 1 ± 4i ) / 8                cancel out 4 top and bottom

x = (1 ± 4i) / 2                    Solutions: x = (1 + 4i) / 2 & x = (1 - 4i) / 2

 

 

Answer 2

x=(-b+/-√(b^2-4ac))/2a

 

So, x=(8+/-√(64-4*1*20))/2

       

        =(8+/-√(-16))/2

 

        =(8+/-4i)/2

 

        =4+/-2i