Final answer:
To solve the equation x^2 + x = 20, we can use the quadratic formula. The solutions are x = 4 and x = -5. Therefore, none of the options listed (A, B, C, D) are true. The correct solutions to the equation x^2 + x = 20 are x = 4 and x = -5.
Step-by-step explanation:
The given equation is x^2 + x = 20. To solve this equation, we can start by rearranging the terms to get x^2 + x - 20 = 0. This is a quadratic equation, and it can be solved by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients in the quadratic equation ax^2 + bx + c = 0.
In this case, a = 1, b = 1, and c = -20.
Plugging these values into the quadratic formula, we get x = (-1 ± √(1^2 - 4(1)(-20))) / (2(1)).
Simplifying further, x = (-1 ± √(1 + 80)) / 2. x = (-1 ± √81) / 2. x = (-1 ± 9) / 2.
So the solutions to the equation are x = (-1 + 9) / 2 = 4 and x = (-1 - 9) / 2 = -5.
Therefore, none of the options listed (A, B, C, D) are true. The correct solutions to the equation x^2 + x = 20 are x = 4 and x = -5.