Solve the quadratic equation 3x2+3x+12=10
. Express its solutions in the form a±bi
To solve the quadratic equation 3x^2 + 3x + 12 = 10 and express its solutions in the form a ± bi, we can follow these steps:
1. Move all the terms to one side of the equation to set it equal to zero:
3x^2 + 3x + 12 - 10 = 0
3x^2 + 3x + 2 = 0
2. Use the quadratic formula to find the solutions. The quadratic formula states that for an equation in the form of ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 3, b = 3, and c = 2. Substituting these values into the quadratic formula, we have:
x = (-3 ± √(3^2 - 4 * 3 * 2)) / (2 * 3)
x = (-3 ± √(9 - 24)) / 6
x = (-3 ± √(-15)) / 6
3. Simplify the expression inside the square root:
√(-15) = √(-1 * 15) = √(-1) * √(15) = i√15
Now, we have:
x = (-3 ± i√15) / 6
The solutions to the quadratic equation 3x^2 + 3x + 12 = 10, expressed in the form a ± bi, are:
x = (-3 + i√15) / 6
x = (-3 - i√15) / 6