Question 389646: Solveby factoring when first coefficient is a negative number. please take me thru each step:
-2x^2 + 13x - 21
they say the answer is 3, 7/2
Answer by texttutoring(324)   (Show Source):
You can put this solution on YOUR website! Recall the general form for a quadratic equation:
ax^2 + bx + c
-2x^2 + 13x - 21
We will use the Decomposition Method for factoring.
First, multiply a*c = (-2)(-21) = 42
So you need to find two numbers that multiply to 42 and add up to the b term, +13. This is pretty easy: the numbers are 7 and 6.
Now the hard part is to decompose the b term, +13, into these two factors. Notice that I list 6x first, so that it pairs with the 2x^2, and the 7x second, so that it pairs with the 21 at the end.
-2x^2 + 13x - 21
-2x^2 + 6x + 7x - 21
Next, factor out the -2x and 7 from each. Note that you are left with identical terms, (x-3) for each.
-2x(x-3) + 7(x-3)
Combine the -2x and 7 into one bracket:
(-2x + 7)(x-3)
This leaves you with two answers, which you can find by setting each bracket to zero, and solving for x:
-2x+7 =0
7=2x
x=7/2
x-3=0
x=3
Hope this helps! Let me know if you're confused by anything.
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