if 13 times a number is subtracted from the square of the number the result is 30. find the number.
x^2 - 13x = 30
now just solve for x.
Hint: 2-15 = -13
To solve this equation, we need to translate the given information into a mathematical equation and then solve for the variable.
Let's assume the number is represented by "x". The first part of the problem states "13 times a number," which can be translated as "13x." The second part states "is subtracted from the square of the number," which can be written as "x^2 - 13x." Finally, the problem states "the result is 30," meaning we set this equal to 30: x^2 - 13x = 30.
Now that we have the equation x^2 - 13x = 30, we can solve it to find the value of x. Rearranging the equation to equal zero, we have x^2 - 13x - 30 = 0.
There are multiple methods to solve this quadratic equation, such as factoring, completing the square, or using the quadratic formula. Let's use factoring:
To factor the quadratic equation x^2 - 13x - 30 = 0, we need to find two numbers whose product is -30 and whose sum is -13. After some trial and error, we can determine that the numbers are -15 and 2.
Therefore, we can rewrite the equation as:
(x - 15)(x + 2) = 0.
Applying the zero product property, we set each factor equal to zero and solve:
x - 15 = 0 or x + 2 = 0.
From the first equation, we find x = 15, and from the second equation, we find x = -2.
So, the solutions to the equation are x = 15 or x = -2.
Therefore, the number can be either 15 or -2.