If 3 times a number is subtracted from the square of the number the result is 30. Find the number
Let the number be x.
The square of the number is x^2.
Three times the number is 3*x.
According to the given information, the equation can be written as:
x^2 - 3x = 30
Rearranging the equation:
x^2 - 3x - 30 = 0
Factoring the quadratic equation:
(x - 6)(x + 5) = 0
Setting each factor equal to zero and solving for x:
x - 6 = 0 or x + 5 = 0
x = 6 or x = -5
Therefore, the number can be either 6 or -5.
Let's assume the number is denoted by 'x'.
According to the given information, "3 times a number is subtracted from the square of the number the result is 30." This can be written as:
x^2 - 3x = 30
Now, let's solve this equation to find the value of 'x'.
Rearranging the equation, we have:
x^2 - 3x - 30 = 0
This quadratic equation can be factored as:
(x - 6)(x + 5) = 0
Setting each factor equal to zero, we get two possible solutions for 'x':
x - 6 = 0 -> x = 6
x + 5 = 0 -> x = -5
Therefore, the two possible numbers that satisfy the given condition are 6 and -5.
Let's solve this problem step by step.
Step 1: Let's assign a variable to the number we are trying to find. Let's call it "x". So, the number we are looking for is "x".
Step 2: According to the problem, "3 times a number is subtracted from the square of the number, and the result is 30". In mathematical terms, this can be written as:
x^2 - 3x = 30
Step 3: Now, we have a quadratic equation. Let's rearrange the equation to bring all terms to one side:
x^2 - 3x - 30 = 0
Step 4: To factorize this quadratic equation, we need to find two numbers whose sum is -3 (the coefficient of x) and whose product is -30 (the constant term). By trial and error, we can determine that -5 and 6 satisfy these conditions.
Therefore, we can write the equation as:
(x - 5)(x + 6) = 0
Step 5: Now, we can set each factor equal to zero and solve for x:
x - 5 = 0 or x + 6 = 0
x = 5 or x = -6
So, the two possible solutions for the number are 5 and -6.
Therefore, the number we are looking for is either 5 or -6.