Find all solutions of the equation and express them in the form
a + bi.
36x^2 − 12x + 2 = 0
18 x^2 - 6 x +1 = 0
x = [6 +/- sqrt ( 36 - 72) ] /36
= [(1/6) +/- sqrt(-1) ]
= 1/6 +/- 1 i
To find the solutions of the given equation, we can use the quadratic formula. The quadratic formula states that for any equation in the form ax^2 + bx + c = 0, the solutions can be found using the following formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In the given equation, we have a = 36, b = -12, and c = 2. Plugging these values into the quadratic formula, we get:
x = (-(-12) ± √((-12)^2 - 4 * 36 * 2)) / (2 * 36)
Simplifying this expression further:
x = (12 ± √(144 - 288)) / 72
x = (12 ± √(-144)) / 72
We have a negative value under the square root (√), which means the solutions will be complex numbers. To simplify the expression, we can rewrite √(-144) as √((-1) * 144) and use the property of imaginary numbers, √(-1) = i.
x = (12 ± √(-1) √(144)) / 72
x = (12 ± 12i) / 72
Now we can simplify this expression further:
x = 12/72 ± 12i/72
x = 1/6 ± i/6
Therefore, the solutions of the equation 36x^2 − 12x + 2 = 0 in the form a + bi are:
x = 1/6 + i/6
x = 1/6 - i/6