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solve quadratic equation by factoring w^2-2w=15

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3 Answers

w2 - 2w = 15
 
Make the equation equal to zero. It becomes
 
w2 - 2w - 15 =0
 
Now we'll expand the equation to get the factors...
- what numbers can be multiplied to give -15 and when subtracted from each other would give -2??
- that would be +3 and -5.
 
so we'll have the equation rewritten as;
 
w2 + 3w - 5w - 15 = 0
 
(w2 + 3w) - (5w - 15) = 0
 
w(w + 3) - 5(w + 3) = 0
 
(w - 5)(w + 3) = 0
 
(w - 5) = 0 or (w + 3) = 0
 
(w - 5) = 0
w - 5 = 0
w = 5
 
or
 
(w + 3) = 0
w + 3 = 0
w = -3
 
RECHECK:
substitute the values of w (5 & -3) in the original equation.
 
w2 - 2w = 15
(5)2 - 2(5) = 15
25 - 10 = 15
15 = 15 .......................so that's correct
 
now we'd use -3
 
w2 - 2w = 15
(-3)2 - 2(-3) = 15
9 + 6 = 15
15 = 15 ..................That's correct too....YAY!!
Denisha,
 
To solve a quadratic equation by factoring, you need to transform the equation into the form:
(x-x1)(x-x2)=0.  The solutions of the quadratic equation are then x1 and x2.
 
In the current problem, you want to begin be moving the constant to the other side of the equation, like this:
 
w2-2w=15
w2-2w-15=0.
 
Next we look at prospective factors of the constant term in the equation, -15.  The possible factor pairs are -15 and 1, -5 and 3, -3 and 5, and -1 and 15.  We choose the factor pair that adds up to the coefficient of the linear term, -2, which in this case is -5 and 3.  And then we factor the quadratic equation using this factor pair:
 
(w-5)(w+3)=0
 
Therefore, the solutions of this quadratic equation are 5 and -3.
Here is the problem worked out and the explanation follows.
 

W2 -2W = 15
 
W2 -2W -15 =0
 
(W-5) (W+3) = 0
 
W-5 = 0    or   w+3 = 0
 
W = 5     or   w= -3
 
To check plug each number into the original equation for each W
 
(5)2 - 2(5) = 15       or     (-3)2 -2(-3) =15
25 -10 =15                        9 +6 =15
15 = 15  YES                         15= 15  YES
 
 
 
To solve by factoring you must first have all of the terms on one side so that the equation is equal to zero.
 
W2 -2W = 15
 
W2 -2W -15 = 15 -15 (subtract 15 from both sides)
 
W2 -2W -15 = 0
 
The exponent of two on the first term tells us that we will have 2 factors (    ) (    )
The last term (-15) being negative tells us our signs will be one positive and one negative (    +   ) (    -   )
Because our signs are one positive and one negative, when we find the factors of the last term (15) we know we will subtract one from the other.
We need to find the factors of -15 so that when we subtract one from the other we get the middle term which is -2. The factors are -5 and 3.
 
(w -5) (w+3) = 0
 
Since the factors multiplied together equal zero, it means either the first factor or the second equal zero so we set each factor = to zero
 
w-5 = 0   or  w+3 = 0     (solve for w)
w= 5       or  w= -3
 
To check see explanation above
 
 
 

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