Question

-x² + x + 6 = 2x + 8. The equation is represented by the system shown here. It is a linear-quadratic equation. This system intersects in _______ zero place(s). Which statement is true?

1) The solution is x = 3.
2) The solutions are x = -2 and x = 3.
3) There are no solutions.
4) There are infinite solutions.

Answer 1

The given equation, -x² + x + 6 = 2x + 8, is a linear-quadratic equation. By rearranging it and using the quadratic formula, we find that the equation has two solutions: x = -1 + √3 and x = -1 - √3.

Step-by-step explanation:

The given equation, -x² + x + 6 = 2x + 8, is a linear-quadratic equation. To solve it, we can rearrange it to get x² + 2x - 2 = 0. This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 2, and c = -2.

Using the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), we substitute the values of a, b, and c: x = (-(2) ± √((2)² - 4(1)(-2))) / (2(1)). Simplifying further, we have x = (-2 ± √(4 + 8)) / 2, which gives us x = (-2 ± √12) / 2. We can simplify the square root to get x = (-2 ± 2√3) / 2.

Simplifying the expression further, x = -1 ± √3. So, the equation has two solutions: x = -1 + √3 and x = -1 - √3.