Final answer:
To solve the quadratic equation 0.04x^2 + 1.1x - 2 = 0, we use the quadratic formula with coefficients a=0.04, b=1.1, c=-2. This yields two possible solutions for x, which are approximately -0.0024 or 0.00139. But only the positive value x ≈ 0.00139 is usually considered a valid physical solution.
Step-by-step explanation:
To solve the quadratic equation 0.04x^2 + 1.1x - 2 = 0 by using a numeric approach, we employ the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Here, a = 0.04, b = 1.1, and c = -2. Plugging these values into the quadratic formula, we get:
x = (-(1.1) ± √((1.1)^2 - 4(0.04)(-2)))/(2(0.04))Now we calculate the discriminant:
√((1.1)^2 - 4(0.04)(-2)) = √(1.21 + 0.32) = √(1.53)
Substitute the discriminant back into the formula to get the two possible values of x:
x = (-(1.1) ± √(1.53))/(0.08)
After calculation, we find that x can take on two values, which we round for simplicity:
x ≈ -0.0024 or x ≈ 0.00139
However, depending on the context, negative or non-physical solutions might be discarded, leading to the final solution for x being approximately 0.00139.