The square of the number is 3 more than half the number,find the possible values of the number

Well, let me put on my "funny hat" and give this a shot!

If I were a number, I would want to be x. Why? Because the square of me (x^2) is 3 more than half of me, which means x^2 = (1/2)x + 3.

Now, let's solve this equation and find the possible values for me!

We can rewrite the equation as x^2 - (1/2)x - 3 = 0.

Hmm, it seems like you might need some serious help with this. But hey, don't worry! I'll solve it for you anyway.

Using the quadratic formula, we find the possible values for me are:

x = (-(-1/2) ± √((-1/2)^2 - 4(1)(-3))) / (2(1))

After some calculations, we get:

x = (1/2 ± √(1/4 + 12)) / 2

Simplifying further, we have:

x = (1/2 ± √(49/4)) / 2

And here comes the grand finale! Drumroll, please!

x = (1 ± 7/2) / 2

Finally, we can conclude that the possible values for me are:

x = (1 + 7/2) / 2, which is 4

x = (1 - 7/2) / 2, which is -3/2

So, there you have it! The possible values of the number are 4 and -3/2. Have fun with them, but remember, numbers can be a little moody sometimes!

Let's denote the number as "x".

According to the given information, the square of the number is 3 more than half the number. Mathematically, we can represent this as:

x^2 = (1/2)x + 3

To find the possible values of the number, we need to solve this equation.

Step 1: Rewrite the equation in standard form:

x^2 - (1/2)x - 3 = 0

Step 2: Factor or use the quadratic formula to solve the equation:

Using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

For the given equation, a = 1, b = -(1/2), and c = -3. Plugging in these values, we get:

x = (-(1/2) ± √((1/2)^2 - 4(1)(-3))) / (2(1))

Simplifying this expression, we have:

x = (-(1/2) ± √(1/4 + 12))/2

x = (-(1/2) ± √(49/4))/2

x = (-(1/2) ± (7/2))/2

Step 3: Solve for x by simplifying the expression:

Case 1: x = (-(1/2) + (7/2))/2 = (6/2)/2 = 3/2

Case 2: x = (-(1/2) - (7/2))/2 = (-8/2)/2 = -4/2 = -2

Therefore, the possible values for the number are 3/2 and -2.

To find the possible values of the number, we need to solve the given equation. Let's denote the number as 'x'.

According to the given condition, the square of the number is 3 more than half the number. Mathematically, we can write this as:

x^2 = (1/2)x + 3

To solve this equation, we can bring all terms to one side to form a quadratic equation:

x^2 - (1/2)x - 3 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

For our equation x^2 - (1/2)x - 3 = 0, the values of a, b, and c are:
a = 1, b = -(1/2), c = -3

Plugging these values into the quadratic formula, we get:

x = (-(1/2) ± sqrt((1/2)^2 - 4(1)(-3))) / (2(1))

Simplifying further:

x = (-1 ± sqrt(1/4 + 12)) / 2

x = (-1 ± sqrt(13/4)) / 2

x = (-1 ± sqrt(13)) / 2

Therefore, the two possible values for the number 'x' are:

x = (-1 + sqrt(13)) / 2

x = (-1 - sqrt(13)) / 2

So, the possible values for the number are (-1 + sqrt(13))/2 and (-1 - sqrt(13))/2.

x = your number

The square of the number is 3 more than half the number mean:

x² = x / 2 + 3

Subtract x / 2 + 3 to both sides

x² - ( x / 2 + 3 ) = x / 2 + 3 - ( x / 2 + 3 )

x² - x / 2 - 3 = 0

Try to solve this equation.

The solutions are:

x = - 3 / 2 and x = 2