Question 167165: Find a value for k that will make 4x^2 + 6.4 x + k a perfect square. Describe the procedure that you used which requires algebra Answer by ptaylor(2198) (Show Source):
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4x^2 + 6.4 x + k-------------------------------------eq1
Let's first assume that the solution is the following and then solve for b:
(2x+b)^2 expand using FOIL;
4x^2+2bx+2bx+b^2=
4x^2+4bx+b^2--------------------Now this equation has to be identical to eq1 in all respects, so:
4b=6.4;
b=6.4/4=3.2/2----eq2
and
b^2=k----------eq3
substitute eq2 into eq3
(3.2/2)^2=k or
k=(3.2/2)^2
substitute k=(3.2/2)^2 into eq1
4x^2+6.4x+(3.2/2)^2=(2x+3.2/2)^2
CK
(2x+3.2/2)^2=4x^2 +(6.4/2)x +(6.4/2)x +(3.2/2)^2=
4x^2+6.4x+(3.2/2)^2
