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What is the exact solution to the equation: 3x^2+6x-4=3?

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted April 2, 2013 at 2:41 AM via web

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What is the exact solution to the equation: 3x^2+6x-4=3?

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jgeertz | College Teacher | (Level 1) Associate Educator

Posted April 2, 2013 at 3:18 AM (Answer #1)

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`3x^2+6x-4=3`

The solutions to this quadratic equation aren't rational and can't be found by factoring. The quadratic formula must be used.

First the equation must be set to zero by moving all terms to the left side.

`3x^2+6x-7=0`

Use the quadratic formula to solve. Here a=3, b=6, c=-7

`x= (-b+-sqrt(b^2-4ac))/(2a)`

`x= (-6+-sqrt(6^2-4(3)(-7)))/(2(3))`

`x=(-6+-2sqrt30)/(2(3))`

`x=(-6+-2sqrt30)/6`

Simplify and solve for the + and - solutions.

`x=(-3+sqrt30)/3`  and  `(-3-sqrt30)/3`

`x = -1 +- sqrt(30)/3`

Both of these answers are exact solutions.

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