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Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting `1` from both sides.

`3x^2 = - 1 - 26`


Subtract 26 from `-1` to get `-27` .

`3x^2 = - 27`


Divide each term in the equation by `3` .

`(3x^2)/3 = -27/3`


Simplify the left-hand side of the equation by canceling the common factors.

`x^2 = - 27/3`


Simplify the equation.

`x^2 = - 9`


Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.

`x = +- sqrt(-9)`


Pull all perfect square roots out from under the radical. In this case, remove the `3i` because it is a perfect square.

`x = +- 3 i`


First, substitute in the `+` portion of the `+-` to find the first solution.

`x=3i `


Next, substitute in the `-` portion of the `+-` to find the second solution.

`x=-3i `


The complete solution is the result of both the `+` and `-` portions of the solution.

`x=3i,-3i`

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Solve `3x^(2) + 1 = -26`

Subtract 1.

`3x^(2) = -27`

Divide by 3.

`x^2 = -9`

Take square root of each side.

`x =sqrt(-9) = ` No real solution, as you cna't take the square root of a negative number.

As a complex number, `sqrt(-9) =sqrt(-1)*sqrt(9)`

Since `sqrt(-1) = i`  , this gives the complex number `3i.`

As a real solution, there is not one.  As a complex number the solution is 3i.

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