Final answer:
The quadratic equation a^2 - 6a + 6 = -2 was rearranged into the standard form and the quadratic formula was used to find two possible values for 'a', which are a = 4 and a = 2.
Step-by-step explanation:
To solve the quadratic equation a^2 - 6a + 6 = -2, we first need to rearrange the equation into the standard form of a quadratic equation ax^2 + bx + c = 0. By adding 2 to both sides of the given equation, we get a^2 - 6a + 8 = 0.
Next, we use the quadratic formula to solve for 'a', which is given by:
-b ± √b^2 - 4ac2a
In the equation a^2 - 6a + 8 = 0, the coefficients are a = 1, b = -6, and c = 8. Plugging these values into the quadratic formula, we get:
-(-6) ± √(-6)^2 - 4×1×82×1
Simplifying the equation:
6 ± √36 - 322
Which simplifies further to:
6 ± √42
Since √4 = 2, we have two possible solutions for 'a':
6 + 22and6 - 22
Thus, the solutions are:
Therefore, by using the quadratic formula, we have found the two possible values of 'a' for the given equation.