Final answer:
The given expression is a quadratic equation, which can be solved using the quadratic formula. Substituting the values and solving the equation yields the solutions x ≈ -1.205 and x ≈ 0.005.
Step-by-step explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b= 14.3, and c = - 20.0. Its solutions are given by the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, the equation is x² + 1.2x - 6.0 × 10-³ = 0. To find the solutions, we substitute the values a = 1, b = 1.2, and c = -6.0 × 10-³ into the quadratic formula and solve for x.
x = (-1.2 ± √((1.2)² - 4(1)(-6.0 × 10-³))) / (2(1))
x = (-1.2 ± √(1.44 + 0.024)) / 2
x = (-1.2 ± √1.464) / 2
x ≈ (-1.2 ± 1.21) / 2
Therefore, the solutions to the equation are approximately x ≈ -1.205 and x ≈ 0.005.