Final answer:
The quadratic equation x² + 1.2 x 10^-2x - 6.0 × 10^-3 = 0 can be solved using the quadratic formula to find two possible values for x. However, recognizing the practical context and equation's constraints, the positive value x = 0.00139 is identified as the correct solution.
Step-by-step explanation:
To find the value of x in this polygon, we are presented with a quadratic equation: x² + 1.2 x 10-2x - 6.0 × 10-3 = 0. Initially, we may attempt to solve this equation using the quadratic formula, which is applicable to equations in the standard form of ax² + bx + c = 0. However, upon closer inspection, it's revealed that the equation is a perfect square, therefore simplifying our process to find x.
When we simplify and rearrange the equation, we observe that x² + 0.0012x - 0.0006 = 0, which allows us to apply the quadratic formula to find the potential values of x. After calculating, we identify two possible solutions for x: x = -0.0024 and x = 0.00139. In certain contexts, negative values may not be applicable, hence the positive value of x = 0.00139 is determined to be the correct solution.
You can explore these concepts in more detail with resources such as the Oxtoby textbook, which provides the numbers needed to solve such equations.