To rewrite the quadratic equation x² + 2x + 3 = 0 in the form x = a ± b, we will first need to use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In our case, the equation is of the form ax² + bx + c = 0, where:
- a = 1
- b = 2
- c = 3
Plugging these values into the quadratic formula:
x = (-(2) ± √((2)² – 4(1)(3))) / (2(1))
This simplifies to:
x = (-2 ± √(4 – 12)) / 2
x = (-2 ± √(-8)) / 2
Since the term under the square root (the discriminant) is negative, we will have imaginary solutions. Continuing with the simplification:
√(-8) = √(8) * i = 2√2 * i
Now substituting back into our equation:
x = (-2 ± 2√2 * i) / 2
Finally, we simplify by dividing each term by 2:
x = -1 ± √2 * i
Thus, we can conclude that in the form x = a ± b, we have:
a = -1 and b = √2 * i.