Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Use the quadratic formula to solve the equation. x^2-4x-3=0
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the equation x^2 - 4x - 3 = 0, we can identify the coefficients a, b, and c as follows:
a = 1
b = -4
c = -3
Now, let's substitute these values into the quadratic formula:
x = (-(-4) ± √((-4)^2 - 4(1)(-3))) / (2(1))
x = (4 ± √(16 + 12)) / 2
x = (4 ± √28) / 2
Simplifying the square root:
x = (4 ± 2√7) / 2
Now, we can simplify further:
x = (2 ± √7)
Therefore, the solutions to the equation x^2 - 4x - 3 = 0 are:
x = 2 + √7
x = 2 - √7