(w+14)/(4w+6)=(3)/(4) show work plz

Mathematics

1 answer:

sergey [27]3 years ago

7 0

Answer:

w = -1.44 and w = -14.06

Step-by-step explanation:

That "(3) / (4)" in (w+14)/(4w+6)=(3)/(4) looks fishy. Assuming that you really meant 3/4, then we have (w+14)/(4w+6)=3/4.

Mult. both sides by 4 to remove the fraction: 4(w+14)/(4w+6) = 3.

Multiply out (w+14)/(4w+6): 4w^2 + 6w + 56w + 84. Combine the w terms, obtaining 4w^2 + 62w + 84. Then the original equation becomes:

4w^2 + 62w + 84 = 3, or 4w^2 + 62w + 81 = 0.

This is a quadratic equation, with a = 4, b = 62 and c = 81. The two roots (values of

w) are as follows:

-62 plus or minus √(62^2-4(4)(81)

----------------------------------------------------------

-62 plus or minus √(2548) -62 plus or minus 50.48

w = ------------------------------------------- = ---------------------------------------

8 8

Simplifying, we get w = -1.44 and w = -14.06

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