Final answer:
To solve the equation g(x) = -7x given that g(x) = -0.6x² + x + 4, we equate the two expressions for g(x), rearrange to form a quadratic equation, and then apply the quadratic formula to find the solutions, which are x = 0.0216 or x = -0.0224.
Step-by-step explanation:
The given equation g(x) = -0.6x² + x + 4 is to be solved under the condition that g(x) = -7x. To find the solution, we set the two expressions for g(x) equal to each other and simplify:
-7x = -0.6x² + x + 4
We then rearrange the equation to have zero on one side, yielding a quadratic equation:
0 = 0.6x² - 8x - 4
Now we can use the quadratic formula to solve for x, where a = 0.6, b = -8, and c = -4. The quadratic formula is:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (8 ± √(64 - 4(0.6)(-4))) / (2*0.6)
Evaluating this further will give us the two possible solutions for x. Following the calculation, we arrive at two values for x which are x = 0.0216 or x = -0.0224.
Because the context of the problem isn't provided, both solutions are considered, unless the context dictates that one of the solutions isn't plausible, such as in a scenario where x represents a quantity that cannot be negative in real life.