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complete the square 4x^2+5x+2

 

Enter your answer in the form a(x+u)^2+v , where  a,u and v are replaced by numbers.

 Jul 23, 2020
 #1
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Complete the square of  4x2 + 5x + 2

 

Step 1:  Separate the  4x2 + 5x  part from the  2:     [ 4x2 + 5x ] + 2

 

Step 2:  Factor out the 4 from the first part:              [ 4(x2 + 5/4x) ] + 2

 

Step 3:  Complete the square of  x2 + 5/4x

              --  Divide  5/4  by 2   --->   5/8

              --  Square this result   --->   25/64

 

Step 4:  Be careful when putting this into the parentheses, because this value will be multiplied by 4, so you'll

              have to subtract out  4 · 25/64  =  25/16  to keep the expression balanced:

                                                                               [ 4(x2 + 5/4x + 25/64) ] + 2 - 25/16

                     

Step 5:  Simplify:  4(x + 5/8)2 + 7/16

 Jul 23, 2020

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