Solve for x. x^2 + (1/2x + 11)^2 = (2x + 1)^2

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`ERRATA ` `CORRIGE:`

My answer above is wrong!

`x=(28+-148)/22` `=(14+- 74)/11`

`x_1= 8` `x_2=-60/11`

`4x^2+4(1/2x+11)^2=4(2x+1)^2`

`4x^2+(x+22)^2=(4x+2)^2`

`4x^2+x^2+44x+484=16x^2+16x+4`

`11x^2-28x-480=0`

`Delta = 784- 4(11)(-480)=21904 >0` exaiats twodifferente solutuionos:

`x=(28+-sqrt(21904))/11` `=(28+-148)/2`

`x_1= 88` `x_2=-60`

Use foil method first.

`x^2 + 1/4x^2 + 11/x + 121 = 4x^2 + 4x + 1`

Multiply both sides by 4 to get rid of the denominator 4.

`4x^2 + x^2 + 44x + 484 = 16x^2 + 16x + 4`

Move the terms on the right side to the left side. Remember to change the signs.

`4x^2 + x^2 + 44x + 484 - 16x^2 - 16x - 4 = 0`

Combine like terms.

`-11x^2 +28x + 480 = 0`

Mmultiply both sides by -1.

`11x^2 - 28x - 480 = 0`

Factor the left side.

`(11x + 60)(x - 8) = 0`

Equate each factor to zero, and solve for x.

`11x + 60 = 0 ; x - 8 = 0`

`11x = -60 ; x = 8`

`x = -60/11 ; x = 8`

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