twice the square of a certain whole number added to 3times the number makes 90. find the number
4? 5? 6? 7?
2x^2 + 3x = 90
now just solve as usual.
To find the number, we can set up an equation based on the given information.
Let's assume the certain whole number is represented by the variable "x".
According to the given information, twice the square of the number is 2x^2, and three times the number is 3x. Adding these two values gives us a total of 2x^2 + 3x.
The problem states that when this sum is equal to 90, so we can write the equation as:
2x^2 + 3x = 90
To solve this quadratic equation, we can rearrange it to the standard form:
2x^2 + 3x - 90 = 0
Now we can proceed to solve the quadratic equation. There are several methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.
In this case, let's solve it by factoring:
2x^2 + 3x - 90 = 0
To factor this quadratic equation, we need to find two numbers that multiply to give -180 (the product of the coefficient of x^2 and the constant term), and add up to give the coefficient of x (which is 3).
After some calculations, we find that the two numbers are 12 and -15. Therefore, the factored form of the equation becomes:
(2x - 15)(x + 12) = 0
Now we set each factor equal to zero and solve for x:
2x - 15 = 0 or x + 12 = 0
Solving these equations, we get:
2x = 15 or x = -12
Dividing both sides of the first equation by 2:
x = 15/2 or x = -12
Since we are given that the number is a whole number, we can disregard the solution x = 15/2, leaving us with the only whole number solution:
x = -12
Therefore, the certain whole number is -12.