Solve the equation 3x^2 -4x = x^2 +2

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve 3x^2 - 4x = x^2 + 2

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

move all the terms to one side

=> 2x^2 - 4x - 2 = 0

=> x^2 - 2x - 1 = 0

x1 = [-b + sqrt(b^2 - 4ac]/2a

=> [2 + sqrt 8]/2

=> 1 + sqrt 2

x2 = 1 - sqrt 2

The required solution of the equation is x = 1+sqrt 2 and x =1- sqrt 2

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equation :

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

We need to find x value that satisfies the equation.

First we will move all terms to the left side so the right side is 0.

==> 3x^2 -4x -x^2 - 2 = 0

==> 2x^2 -4x -2 = 0

Now we will divide by 2.

==> x^2 - 2x -1 = 0

Now we will use the formula to find the roots.

==> x1= ( 2 + sqrt(4+4) / 2 = (2+ sqrt8)/2 = (2+2sqrt2)/2 = 1+sqrt2

==> x2= (1-sqrt2)

Then the values of x that satisfies the equation are :

x= { (1+sqrt2) , (1-sqrt2) }

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