SOLUTION: Can you please help me with this problem? I am stumped!
Find a value for k that will make 4x^2+6.4x+k a perfect square. I need to describe the procedure that I used.
All I
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-> SOLUTION: Can you please help me with this problem? I am stumped!
Find a value for k that will make 4x^2+6.4x+k a perfect square. I need to describe the procedure that I used.
All I
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Question 163331: Can you please help me with this problem? I am stumped!
Find a value for k that will make 4x^2+6.4x+k a perfect square. I need to describe the procedure that I used.
All I can figure so far is:
k=?
4x^2+6.4x+k Found 2 solutions by ptaylor, ankor@dixie-net.com:Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! 4x^2+6.4x+k=0 divide each term by 4
x^2+(6.4/4)x+k/4=0----eq1
Let (x+a)^2 be the solution to this quadratic
expand, using foil:
x^2+xa+xa+a^2=
x^2+2xa+a^2=0-------eq2
Now we know that eq2 has to be identical to eq1 in all respects, so:
2a=(6.4/4) divide each side by 2
a=(6.4/8)-------eq3
a^2=k/4-----------eq4
substitute eq3 into eq4
(6.4/8)^2=k/4 or
40.96/64=k/4 multiply each side by 4
k=40.96/16
CK
x^2+(6.4/4)x+(40.96/64)
(x+6.4/8)^2 expand using foil
x^2+(6.4/8)x+(6.4/8)x+(6.4/8)^2=
x^2+(6.4/4)x+40.96/64
We can work this problem without dividing each term by 4 as we did initially.
4x^2+6.4x+k----------------eq1a
Let (ax+b)^2 be the solution ( a perfect square) expand using foil
a^2x^2+abx+abx+b^2 or
a^2x^2+2abx+b^2-----again, this must be identical to eq1a, so:
a^2=4-------------eq2a
2ab=6.4-----------eq3a divide each side by 2a
b=6.4/2a-------substitute this into eq4a
and b^2=k-----eq4a
(6.4/2a)^2=k
(40.96/4a^2)=k but from eq2a, a^2=4, therefore
k=(40.96/16)-------------------------same as before
Hope this helps---ptaylor
You can put this solution on YOUR website! Find a value for k that will make 4x^2 + 6.4x + k a perfect square. I need to describe the procedure that I used.
:
We want the coefficient of x^2 to be 1, divide equation by 4, resulting in:
x^2 + 1.6x +
:
To find the 3rd term, divide the coefficient of x by 2 and square it = = .64
k = 4*.64
k = 2.56
:
The equation: 4x^2 + 6.4x + 2.56 which is (2x + 1.6)^2
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