To solve the equation x² – 2x – 20 = 0 using the quadratic formula, we need to identify the coefficients in the standard form of the quadratic equation, which is ax² + bx + c = 0.
In our equation, we have:
- a = 1
- b = -2
- c = -20
The quadratic formula is given by:
x = (-b ± √(b² – 4ac)) / (2a)
First, we compute the discriminant (the part under the square root):
b² – 4ac = (-2)² – 4(1)(-20) = 4 + 80 = 84.
Now, we can substitute the values into the quadratic formula:
x = (2 ± √84) / 2
To simplify further, we first find the square root of 84:
√84 can be simplified as √(4 × 21) = 2√21.
This gives us:
x = (2 ± 2√21) / 2
x = 1 ± √21
Thus, the two possible values of x are:
- x = 1 + √21
- x = 1 – √21
In decimal form, these approximate values are:
- x ≈ 5.58
- x ≈ -3.58
So, the final answers for the values of x are:
- x ≈ 5.58
- x ≈ -3.58