when three times a number is added to a square of a number the result is ten,find the number.
To solve this problem, let's break it down into steps:
Step 1: Assign variables:
Let's assume the number we're looking for is 'x.'
Step 2: Set up the equation:
According to the problem, "when three times a number is added to a square of a number, the result is ten." This can be written as an equation:
3x + x^2 = 10
Step 3: Simplify the equation:
Rearrange the equation in order to simplify it:
x^2 + 3x - 10 = 0
Step 4: Solve the equation:
To find the value of 'x,' we need to solve the quadratic equation.
There are multiple methods to solve it, but let's use factoring:
Factoring the quadratic equation:
(x + 5)(x - 2) = 0
Setting each factor to zero:
x + 5 = 0 --> x = -5
x - 2 = 0 --> x = 2
Thus, the two possible solutions for 'x' are -5 and 2.
Therefore, the number can be either -5 or 2.