Solve the equation by factoring 2x^2+7x=4
2 answers:
Answer:
x = - 4 , x =
Step-by-step explanation:
given 2x² + 7x = 4
rearrange into standard form : ax² + bx + c = 0 : a ≠ 0
subtract 4 from both sides
2x² + 7x - 4 = 0 ← in standard form
Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term, that is
product = 2 × - 4 = - 8 and sum = + 7
The factors are + 8 and - 1
use these factors to split the middle term
2x² + 8x - x - 4 = 0 ( factor by grouping first/second and third/fourth terms )
2x(x + 4) - 1(x + 4) = 0 ( take out the common factor (x + 4) )
(x + 4)(2x - 1) = 0
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
2x - 1 = 0 ⇒ 2x = 1 ⇒ x =
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Answer:
8c2 = 28
Step-by-step explanation:
You can plug this into your calculator (on a TI-84, it's MATH -> PRB -> 3) as 8 nCr 2.
Let's try to understand what the output means, though! The nCr function is based on Pascal's Triangle (see the attachment for a picture).
When we do 8 choose 2, we are basically thinking about having 8 possible values and 2 spots to fit them in, and we don't care about what order they're in. The probability of this is 8*7 / 2 = 28. Our answer makes sense!
