Final answer:
To find the value of x for the expression (6x + 7)(11x - 2), set it equal to a specific value or condition, resulting in a quadratic equation. Solve this using the quadratic formula to get two potential solutions, and determine the reasonable one in context.
Step-by-step explanation:
The value of x when the expression (6x + 7)(11x - 2) equals a specific value is determined by first setting the expression equal to that specific value or condition, resulting in a quadratic equation. The equation derived from this expression will typically have the form ax² + bx + c = 0, where a, b, and c are coefficients that derive from expanding and simplifying the expression and the given condition.
To solve for x, we can employ the quadratic formula x = (-b ± √(b² - 4ac))/(2a). This formula provides two potential values for x, which are usually checked for reasonableness in the context of the problem. Typically, one solution is found to be the valid answer. If confronted with an equation like x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0, you can apply this method to find the value(s) of x.