What is the solution set to the following equation? 4m^2-8m+9=0

m =(8-√-80)/8=1-i/2√ 5 = 1.0000-1.1180i

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22m2 -  8m) -  -9  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4m2-8m+9  

The first term is,  4m2  its coefficient is  4 .

The middle term is,  -8m  its coefficient is  -8 .

The last term, "the constant", is  +9  

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36  

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -8 .

     -36    +    -1    =    -37  

     -18    +    -2    =    -20  

     -12    +    -3    =    -15  

     -9    +    -4    =    -13  

     -6    +    -6    =    -12  

     -4    +    -9    =    -13  

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  2  :

 4m2 - 8m + 9  = 0  

Step  3  :

Parabola, Finding the Vertex :

3.1      Find the Vertex of   y = 4m2-8m+9

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answer is:

1.75 pounds