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Solve this equation using the quadratic formula.  3x^2 -5 = -8x -10

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted May 23, 2013 at 2:46 PM via web

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Solve this equation using the quadratic formula. 

3x^2 -5 = -8x -10

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 23, 2013 at 3:25 PM (Answer #1)

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Solve `3x^2-5=-8x-10` using the quadratic formula:

The quadratic formula is : if `ax^2+bx+c=0 "then" x=(-b+-sqrt(b^2-4ac))/(2a)`

We must rewrite in standard form:

`3x^2+8x+5=0` Now a=3,b=8, and c=5 so:

`x=(-8+-sqrt(8^2-4(3)(5)))/(2(3))`

`=(-8+-sqrt(4))/6`

`=-4/3+1/3=-1`

or

`=-4/3-1/3=-5/3`

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The solutions are `x=-1,-5/3`

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You could factor:

`3x^2+8x+5=(3x+5)(x+1)` and find the roots that way also.

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oldnick | (Level 1) Valedictorian

Posted May 23, 2013 at 4:34 PM (Answer #2)

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`3x^2-5=-8x-10`

`3x^2+8x+5=0`

`3x^2+3x+5x+5=0`

`3x(x+1)+5(x+1)=0`

`(3x+5)(x+1)=0`

`3x+5=0 rArr x=-5/3`

`x+1=0 rArr x=-1`

So solutions are  `x_1=-1``x_2=-5/3`

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