If: 3w = 42 Then: w = 14
To factor 4w^2 + 12w + 4 = 0, first divide the equation by 4 to simplify it: w^2 + 3w + 1 = 0. Then, decompose the middle term (3w) into two terms whose product is the product of the coefficient of w^2 and the constant term (1): (w+1)(w+1) = 0. Therefore, the factors are (w+1)(w+1) = 0.
w2-3w = 0 w(w-3) = 0 w = 3 or w = 0
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3w^2 - 8w + 4 = (3w -2) (w-2) So 3w-2=0, then 3w=2, so w=2/3, w-2=0, so w=2. Your solutions are w=2/3 and w=2.
you do 2 sets of parenthesis and check it. for example: w2(w squared)-7w-8 (w+1) (w-8) *if you add 1w and -8w you will get -7w, which is what they want you to get. and w & w multiply to get w2(w squared), which is also what the factoring wants. another example: 3w2 (3w squared)+2-8 (3w-4) (w+2) *same thing applies with 3w x w = 3w2, and -4 +2=2, which is the answer. use this theory in all of them, unless there is a greatest common factor (GCF).
If: 3w = 42 Then: w = 14
To factor 4w^2 + 12w + 4 = 0, first divide the equation by 4 to simplify it: w^2 + 3w + 1 = 0. Then, decompose the middle term (3w) into two terms whose product is the product of the coefficient of w^2 and the constant term (1): (w+1)(w+1) = 0. Therefore, the factors are (w+1)(w+1) = 0.
3w -6 = -15 3w = -15+6 3w = -9 w = -3
If: 3w-17 = 4 Then: w = 7
3w - 2 = 2w + 3 Add 2 to both sides: 3w = 2w + 5 Subtract 2w from both sides: w = 5
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w2-3w = 0 w(w-3) = 0 w = 3 or w = 0
33
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1. L + W = P/2 = 300 so L = 300 - W; 2. L = 3W + 2 so 300 - W = 3W + 2 ie 4W = 298 making W = 74.5 and L 225.5