Answer:
However, Stephanie is thinking of a positive number, so the answer is x = 5/2, or 2.5 as a decimal.
Explanation:
Let's call the positive number that Stephanie is thinking of "x."
According to the information given:
1. She squares the number, which means x^2.
2. She multiplies the result by 6, so we have 6x^2.
3. She then adds her original number, which is x.
So, we can create an equation based on these steps:
6x^2 + x = 40
Now, let's solve this quadratic equation:
6x^2 + x - 40 = 0
To simplify this equation, let's multiply the entire equation by 2 to eliminate the decimal coefficients:
12x^2 + 2x - 80 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 12, b = 2, and c = -80. Plugging these values into the quadratic formula:
x = (-2 ± √(2² - 4 * 12 * (-80))) / (2 * 12)
x = (-2 ± √(4 + 3840)) / 24
x = (-2 ± √3844) / 24
Now, let's simplify the square root:
x = (-2 ± 62) / 24
We have two potential solutions:
1. x = (-2 + 62) / 24 = 60 / 24 = 5/2
2. x = (-2 - 62) / 24 = -64 / 24 = -8/3
However, Stephanie is thinking of a positive number, so the answer is x = 5/2, or 2.5 as a decimal.