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Solve for x.  2x^2-9x+7=0

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted April 3, 2013 at 4:59 PM via web

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Solve for x. 

2x^2-9x+7=0

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 3, 2013 at 5:47 PM (Answer #1)

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You need to find the solutions to the given quadratic equation, hencem you may use quadratic formula such that:

`x_(1,2) = (-b+-sqrt(b^2 - 4ac))/(2a)`

Identifying the coefficients a,b,c yields:

`a = 2, b = -9, c = 7`

`x_(1,2) = (9 +- sqrt((-9)^2 - 4*2*7))/(2*2)`

`x_(1,2) = (9 +- sqrt(81 - 56))/4`

`x_(1,2) = (9 +- sqrt25)/4 => {(x_1 = (9 + 5)/4),(x_2 = (9 - 5)/4):}`

`x_1 = 7/2; x_2 = 1`

Hence, evaluating the solutions to quadratic equation, yields `x_1 = 7/2; x_2 = 1.`

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pramodpandey | College Teacher | Valedictorian

Posted April 4, 2013 at 7:05 AM (Answer #2)

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`2x^2-9x+7=0`

Let us factorize it by spliting middle term

`2x^2-7x-2x+7=0`

`x(2x-7)-1(2x-7)=0`

`(2x-7)(x-1)=0`

`So either 2x-7=0 or x-1=0`

`2x-7=0`

`x=7/2 `

`x=1`

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