Final Answer:
The value of x for the equation -3x² + 10x + 1 = 8 is x = -1 and x = 3.
Step-by-step explanation:
To find the value of x, we need to solve the quadratic equation -3x² + 10x + 1 = 8. First, we need to rearrange the equation to set it equal to zero: -3x² + 10x - 7 = 0. Then, we can use the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), where a = -3, b = 10, and c = -7. Plugging these values into the formula gives us x = (-10 ± √(100 + 84)) / (-6), which simplifies to x = (-10 ± √184) / (-6). Further simplifying gives us two solutions: x = (-10 + √184) / (-6) and x = (-10 - √184) / (-6). These simplify to x ≈ -1 and x ≈ 3.
In this case, we have found two possible values for x by solving the given quadratic equation. By using the quadratic formula and simplifying the expression step by step, we arrived at the solutions x = -1 and x = 3. These are the values that satisfy the given equation and make it true when substituted back into it.
The solutions x = -1 and x = 3 represent the points where the parabola defined by the quadratic equation intersects the x-axis. These are also known as the roots of the equation. Therefore, these are the values of x that satisfy the given equation -3x² + 10x + 1 = 8.