Five times of a positive whole numbers 3 less than twice the square of...
Finding Five Times a Positive Whole Number 3 Less than Twice the Square of the Number
To find five times a positive whole number 3 less than twice the square of the number, we need to follow the given steps:
Step 1: Understand the problem
Before solving the problem, let's first understand what the question is asking. The problem states that we need to find five times a positive whole number. This means we need to multiply the number by 5. However, the number is not given directly. Instead, we are given a condition that the number is 3 less than twice the square of the number. To find the number, we need to solve this condition.
Step 2: Translate the condition into an equation
We can translate the given condition as:
Number = 2 × (Number)² – 3
This is because the number is 3 less than twice the square of the number. The square of the number is (number)². Twice the square of the number is 2 × (number)². Therefore, the number is 3 less than 2 × (number)².
Step 3: Solve the equation
We can simplify the equation as:
(Number)² – 2 × (Number) + 3 = 0
This is a quadratic equation. We can solve it using the quadratic formula:
Number = [2 ± sqrt(4 – 4 × 1 × 3)] / 2
Number = [2 ± sqrt(4 – 12)] / 2
Number = [2 ± sqrt(-8)] / 2
Number = 1 ± sqrt(2) i
Since the number has to be a positive whole number, we can discard the negative root and take the positive root:
Number = 1 + sqrt(2) ≈ 2.4
However, 2.4 is not a whole number. Therefore, there is no solution to this problem.
Step 4: Conclusion
In conclusion, we cannot find five times a positive whole number 3 less than twice the square of the number because there is no such number that satisfies the given condition. The problem is unsolvable.