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Solve this equation using the quadratic formula:  (2x-3)^2 - 14 = 2x(x-7)

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted May 16, 2013 at 5:03 PM via web

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Solve this equation using the quadratic formula: 

(2x-3)^2 - 14 = 2x(x-7)

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 16, 2013 at 5:23 PM (Answer #1)

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First, we need to simpify the equation to standard form `(ax^2+bx+c)` :

Expand the squared term:

`(2x-3)(2x-3)-14=2x(x-7)`

Next expand the multiplication:

`4x^2-6x-6x+9-14=2x^2-14x`

Finally, move all terms to the left side and collect like terms:

`4x^2-2x^2-12x+14x-5=0`

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

We can now solve for the roots of this equation using the quadratic formula:

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

a=2; b=2; c=-5

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

`x=(-2+-sqrt(44))/4`

`x_1=(-2+sqrt(44))/4 =1.16`  

`x_2=(-2-sqrt(44))/4=-2.16`

Graph of the function:

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