Problem

$x^{2}+12 x-12 y+12=0$

Answer

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Answer

\(\boxed{x = -2\sqrt{3y + 6} - 6, x = 2\sqrt{3y + 6} - 6}\) are the roots of the quadratic equation.

Steps

Step 1 :We are given the quadratic equation \(x^{2}+12 x-12 y+12=0\).

Step 2 :We can solve this equation using the quadratic formula, which is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where a, b, and c are the coefficients of the quadratic equation in the form \(ax^2 + bx + c = 0\).

Step 3 :In this case, a = 1, b = 12, and c = -12y + 12.

Step 4 :Substituting these values into the quadratic formula, we get the solutions \(x = -2\sqrt{3y + 6} - 6\) and \(x = 2\sqrt{3y + 6} - 6\).

Step 5 :\(\boxed{x = -2\sqrt{3y + 6} - 6, x = 2\sqrt{3y + 6} - 6}\) are the roots of the quadratic equation.

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