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Answer:
To find the solution set of the quadratic equation 6x^2 - 30 = 36, we first need to simplify the equation by moving all terms to one side to set it equal to zero.
Given equation: 6x^2 - 30 = 36
Subtract 36 from both sides:
6x^2 - 30 - 36 = 0
6x^2 - 66 = 0
Now, the equation is in the form ax^2 + bx + c = 0, where a = 6, b = 0, and c = -66.
The next step is to solve the quadratic equation. We can use the quadratic formula to find the solutions:
The quadratic formula is:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Substitute the values of a, b, and c into the formula:
x = \frac{-0 \pm \sqrt{0 - 4(6)(-66)}}{2(6)}
x = \frac{\pm \sqrt{1584}}{12}
x = \frac{\pm 2\sqrt{396}}{12}
x = \frac{\pm 2\sqrt{4 \times 99}}{12}
x = \frac{\pm 4\sqrt{99}}{12}
x = \frac{\pm 4\sqrt{9 \times 11}}{12}
x = \frac{\pm 4 \times 3\sqrt{11}}{12}
x = \frac{\pm 12\sqrt{11}}{12}
x = \pm \sqrt{11}
Therefore, the solution set of the equation 6x^2 - 30 = 36 is:
x = \pm \sqrt{11}