The square of a number is 3 more than half the number.find the possible values of the number.
n^2 = 3 + 0.5n
I didn't get it well
Let's break down the information given step by step to find the possible values of the number.
Step 1: Let's define the number as "x".
Step 2: The square of the number is x^2.
Step 3: Half the number is x/2.
Step 4: Three more than half the number is x/2 + 3.
Step 5: According to the information given, the square of the number is 3 more than half the number. So, we can set up the equation: x^2 = x/2 + 3.
Step 6: To solve the equation, let's multiply everything by 2 to eliminate the fraction: 2(x^2) = 2(x/2 + 3).
Step 7: Simplifying the equation further: 2x^2 = x + 6.
Step 8: Rearranging terms in the equation: 2x^2 - x - 6 = 0.
Step 9: Factoring the equation by splitting the middle term: (2x + 3)(x - 2) = 0.
Step 10: Setting each factor equal to zero and solving for x:
2x + 3 = 0 -> 2x = -3 -> x = -3/2.
x - 2 = 0 -> x = 2.
Step 11: Therefore, the possible values of the number are x = -3/2 and x = 2.
In conclusion, the number can be either -3/2 or 2.
To solve this problem, we'll use algebraic equations.
Let's assume that the number we are looking for is "x".
According to the problem, the square of the number is 3 more than half the number:
x^2 = (1/2)x + 3
To find the possible values of x, we will rearrange the equation and solve for x.
First, let's get rid of the fraction by multiplying both sides of the equation by 2:
2x^2 = x + 6
Now, let's rearrange the equation to obtain a quadratic equation:
2x^2 - x - 6 = 0
To solve this equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:
(2x + 3)(x - 2) = 0
Setting each factor equal to zero, we get two possible solutions:
2x + 3 = 0 or x - 2 = 0
Solving each of these equations, we find:
2x = -3 or x = 2
Dividing both sides of the first equation by 2, we find:
x = -3/2
Therefore, the possible values of x are:
x = -3/2 or x = 2