one postive number is 9 more than twice a number if product is 893 find the numbers
If x = one number, then the other is 2x + 9.
x(2x + 9) = 893
Solve for x.
first number ---- x
second number -- 2x+9
x(2x+9) = 893
2x^2 + 9x - 893 = 0
x = (-9 ± √7225)/4
x = 19 or x = a negative
so the numbers are 19 and 47
check: 19x47 = 893
Let's denote the unknown number as "x." According to the given information, one positive number is 9 more than twice the unknown number. Mathematically, this can be represented as:
One positive number = 2x + 9
The problem also states that the product of the two numbers is equal to 893. Mathematically, this can be written as:
x * (2x + 9) = 893
To solve this equation and find the value of "x," we need to follow these steps:
Step 1: Expand the equation by multiplying x with 2x + 9:
2x^2 + 9x = 893
Step 2: Move all the terms to one side of the equation:
2x^2 + 9x - 893 = 0
Step 3: To solve this quadratic equation, you can either factor it or use the quadratic formula. Since factoring might not be straightforward, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = 9, and c = -893.
Substituting these values into the formula, we have:
x = (-9 ± √(9^2 - 4 * 2 * -893)) / (2 * 2)
Simplifying the equation further:
x = (-9 ± √(81 + 7136)) / 4
x = (-9 ± √7217) / 4
Now, we calculate the two possible values of "x" by using both the positive and negative square root:
x₁ = (-9 + √7217) / 4
x₂ = (-9 - √7217) / 4
These two values will give us the two numbers we are looking for.