Think of a number square it add 2 times the original number the result is 80 find the number
x^2 + 2x = 80
Let's solve this step-by-step:
1. Let's assume the number is represented by 'x'.
2. The square of x is x^2.
3. Adding 2 times the original number to the square gives us the equation: x^2 + 2x.
4. According to the problem, the result of x^2 + 2x is 80. So our equation becomes: x^2 + 2x = 80.
5. To solve this quadratic equation, we need to set it equal to zero by subtracting 80 from both sides: x^2 + 2x - 80 = 0.
6. Now, we can factor this equation: (x + 10)(x - 8) = 0.
7. Setting each factor equal to zero, we have two possible solutions:
- x + 10 = 0, which gives us x = -10.
- x - 8 = 0, which gives us x = 8.
8. Therefore, the two possible numbers are x = -10 and x = 8.
However, since the problem states that the number is "the original number" and positive numbers are often assumed to be the intended solution when they're not specified, the answer is x = 8.