Find the solutions of the following quadratic equation.
x squared minus 4 x minus 6 equals 0
(1 point)
Responses
x equals 4 plus Start Root 10 End Root or x equals 4 minus Start Root 10 End Root
Image with alt text: x equals 4 plus Start Root 10 End Root or Image with alt text: x equals 4 minus Start Root 10 End Root
x equals 2 plus Start Root 10 End Root or x equals 2 minus Start Root 10 End Root
Image with alt text: x equals 2 plus Start Root 10 End Root or Image with alt text: x equals 2 minus Start Root 10 End Root
x equals 2 plus Start Root 6 End Root or x equals 2 minus Start Root 6 End Root
Image with alt text: x equals 2 plus Start Root 6 End Root or Image with alt text: x equals 2 minus Start Root 6 End Root
x equals 4 plus Start Root 6 End Root or x equals 4 minus Start Root 6 End Root
The solutions of the quadratic equation x^2 - 4x - 6 = 0 are x = 2 + √10 or x = 2 - √10.
To find the solutions of the quadratic equation, you can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the quadratic equation is x^2 - 4x - 6 = 0, which can be rewritten in the standard form as ax^2 + bx + c = 0:
a = 1, b = -4, c = -6
Now, substitute the values of a, b, and c into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(1)(-6))) / (2(1))
Simplifying:
x = (4 ± √(16 + 24)) / 2
x = (4 ± √40) / 2
x = (4 ± 2√10) / 2
Now, simplify the expression:
x = 2 ± √10
Therefore, the solutions of the quadratic equation x^2 - 4x - 6 = 0 are:
x = 2 + √10 or x = 2 - √10