Solve the quadratic equation:

(1/2x + 3)^2 + 6 = 19

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(1/2x+3)^2 = 13

1/2x+3 = +/- sqrt 13

1/2x = 3 +/- sqrt 13

x = 6 +/- 2 sqrt 13

`(1/2 x+3)^2 +6=19`

`(1/2x+3)^2=19-6`

`(1/2 x+3)^2= 13`

`1/2x+3=+-sqrt(13)`

`1/2x=-3+-sqrt(13)`

`x=2(-3+-sqrt(13))`

`x_1=1.2111025509279`

`x_2= -13.211025509279`

Solve `(1/2x+3)^2+6=19` :

`(1/2x+3)^2+6=19` Subtract 6 from both sides

`(1/2x+3)^2=13` Take the square root of both sides

`(1/2x+3)=+-sqrt(13)` Subtract 3 from both sides

`1/2x=-3+-sqrt(13)` Multiply both sides by 2

`x=-6+-2sqrt(13)`

**The solutions are** `x=-6+sqrt(13),x=-6-sqrt(13)`

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** The x values are approximately x=1.211,x=-13.211

The graph of the left side in black, y=19 in red:

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