When three times a number is added to the square of the number,the result is ten,find the number.

3n+n^2=10

n^2+3n-10=0
(N-2)(n+5)=0
n= 2, or -5

i dont understand please

To solve this problem, let's break it down step by step.

Step 1: First, let's assign a variable to the unknown number. Let's call it "x".

Step 2: According to the problem, "three times a number is added to the square of the number, the result is ten." Mathematically, we can write this as an equation: 3x + x^2 = 10.

Step 3: Now, we have a quadratic equation. Let's rearrange it to get it into standard form: x^2 + 3x - 10 = 0.

Step 4: To solve this quadratic equation, we can factor it or use the quadratic formula. Since this equation can be factored easily, let's factor it: (x + 5)(x - 2) = 0.

Step 5: Now, we can set each factor equal to zero and solve for x:
x + 5 = 0 or x - 2 = 0

Step 6: Solving for x in each equation:
For x + 5 = 0, we have x = -5.
For x - 2 = 0, we have x = 2.

Step 7: The two possible solutions for x are -5 and 2. Therefore, the number could be either -5 or 2.