Solve each equation using the quadratic formula. (Enter your answers as a comma-separated list.)
x^2-2x+2=0
2 + 2x − x2 = 0
Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.)
2 + 2x − x2 = 0
To solve the equation x^2 - 2x + 2 = 0 using the quadratic formula, we need to identify the coefficients a, b, and c.
In this case, a = 1, b = -2, and c = 2.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the given values, we get:
x = (-(-2) ± √((-2)^2 - 4(1)(2))) / (2(1))
x = (2 ± √(4 - 8)) / 2
x = (2 ± √(-4)) / 2
Since we have a negative number under the square root, √(-4), the equation does not have real solutions. This means that the quadratic formula will give us complex solutions.
Using complex numbers, we can simplify the square root of -4:
√(-4) = √(4 * (-1)) = √(4) * √(-1) = 2i
Now we can rewrite the equation:
x = (2 ± 2i) / 2
Simplifying further, we get:
x = 1 ± i
Therefore, the solutions to the equation x^2 - 2x + 2 = 0 using the quadratic formula are:
x = 1 + i, 1 - i
x^2 - 2x + 2 = 0
X = (-B +- sqrt(B^2-4AC))/2A
X = (2 +- sqrt(4-8))/2
X = (2 +- sqrt(-4))/2
X = (2 +- sqrt(4(-1))/2
X = (2 +- 2sqrt(-1)/2
X = (2 +- 2i)/2 = 1 +- i = 1+i, and 1-i.
Check:
(1+i)^2 - 2(1+i) + 2 =
1 + 2i - 1 - 2 -2i + 2 = 0