Question 620: I need help on this equation please
2x² + 5x - 3 = 0
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! >>I need help on this equation please<<
`
2x² + 5x - 3 = 0
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2 can only be factored into two factors as 1×2.
3 can only be factored into two factors as 1×3.
`
So the only possible ways we could have for the factorization of the
left side are:
`
(2x ` 3)(x ` 1)
(2x ` 1)(x ` 3)
`
The signs must be opposite so that we get -3 for the last term,
so we have these possibilities:
(2x + 3)(x - 1) = 2x² + x - 3
(2x - 3)(x + 1) = 2x² - x - 3
(2x + 1)(x - 3) = 2x² - 5x - 3
`
Only the last is correct. So we have
`
` ` 2x² + 5x - 3 = 0
`(2x - 1)(x + 3) = 0
`
Using the zero-factor property, either of the parenthetical expressions
can equal zero.
`
Setting the first = 0
2x - 1 = 0
` ` 2x = 1
` ` ` x = 1/2
`
Setting the second = 0
`x + 3 = 0
` ` ` x = -3
`
So the solution set is {1/2, -3}
`
AnlytcPhil
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