We are looking for k in the equation
(x+4)(x+k/4) = x^2+7x+k
The left hand side expands to:
x^2+(4+k/4)x+k = x^2+7x+k
Comparing coefficients for the linear terms, we have the equation
(4+k/4)=7
Solving for k:
16+k=28
k=12
Thus the number to be subtracted is 15-k=15-12=3
Explanation:
The Law of Cosines specifies the relationship between the three sides of a triangle and any one of the angles. If the sides are designated a, b, and c, and the angle opposite side c is C, then it tells you ...
c² = a² + b² -2ab·cos(C)
This relationship can be used to find any and all angles, given the three sides of a triangle. Or, having found one angle using the Law of Cosines, the others can be found using the Law of Sines:
sin(A)/a = sin(B)/b = sin(C)/c
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Typically, inverse functions are required. That is, from the Law of Cosines, ...
C = arccos((a² +b² -c²)/(2ab))
And from the Law of Sines, ...
A = arcsin(a/c·sin(C))
B = arcsin(b/c·sin(C))
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<em>Note on solving triangles</em>
It often works best to make use of exact values where possible. It is also a good idea to start with the longest side/largest angle. Of course, once you have two angles the other can be found as the supplement of their sum.
By multiplying fractions, you aren't changing any of them. For example 1/2 times 1/3 all you do is multiply. But to add 1/2 and 1/3 you would have to get a common denominator.<span />
