What number or numbers can subtract two times a number from half of its square and gives a result of 16
x^2/2 - 2x = 16
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Can u give me the answer so I know how to do the other questions
What number or numbers can subtract two times a number from half of its square and gives a result of 16
To solve this problem, we will set up an equation based on the information given.
Let's start by breaking down the problem step by step:
1. "Two times a number": Let's assume the number is represented by the variable 'x'. So, two times the number will be 2x.
2. "Half of its square": Squaring the number 'x' gives us x^2, and half of its square will be (1/2)(x^2).
3. "Subtract two times a number from half of its square": This can be expressed as (1/2)(x^2) - 2x.
According to the problem, this expression should result in 16. Therefore, we set up the equation:
(1/2)(x^2) - 2x = 16
Now, we can solve the equation to find the value(s) of 'x':
(1/2)(x^2) - 2x = 16
Multiply both sides of the equation by 2 to eliminate the fraction:
x^2 - 4x = 32
Rearrange the equation:
x^2 - 4x - 32 = 0
Now, we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:
(x + 4)(x - 8) = 0
This gives us two possibilities:
1. x + 4 = 0, which implies x = -4
2. x - 8 = 0, which implies x = 8
So, the value(s) of 'x' that satisfy the equation and give a result of 16 are -4 and 8.
Therefore, the number or numbers that can be subtracted from twice the number to get 16 are -4 and 8.