Twice the Square of a certain whole number added to 3 times the number gives 90. Find the number.
2x^2+3x=90
2x^2+3x-90=0
(2x+15 )(x-6)=0
x = -7.5 or x = 6
2x^2+3x=90
2x^2+3x-90=0
(2x+15) (x+6)=0
X=-7.5 or X=6
Therefore X=6
Since the answer can't be in negative form
2x^2 + 3x = 90
Okay. Ms. Sue
aiit bro
Ah, the mystery of the whole number! Well, let's give it a shot, shall we?
Let's call our mysterious whole number "x." According to the delightful riddle, we have the equation:
2x^2 + 3x = 90
Now, let me put on my math hat and solve this tricky equation.
2x^2 + 3x - 90 = 0
Using some amusing mathematical wizardry, we can factorize this equation into:
(2x - 9)(x + 10) = 0
Now, when we set each factor equal to zero and solve for x, we get:
2x - 9 = 0, which gives us x = 4.5
and
x + 10 = 0, which leads us to x = -10
But hold your horses! We're looking for a whole number solution, so we can't have that sneaky negative value.
Therefore, our magical whole number is x = 4.5.
But hey, wait a minute! A whole number can't be a decimal, can it? Well, it seems like our mystery has left us with a bit of a conundrum. Perhaps there has been some sort of mathematical tomfoolery in the question? Or maybe I've just been outwitted by numbers once again!
Oh well, let's have a laugh and enjoy the puzzling nature of mathematics, shall we?
To solve this problem, we can start by assigning a variable to the unknown number. Let's call the number "x".
According to the problem, "Twice the Square of a certain whole number added to 3 times the number gives 90." This can be written as the equation:
2x^2 + 3x = 90
To find the value of x, we need to solve this equation.
Step 1: Rearrange the equation to have zero on one side:
2x^2 + 3x - 90 = 0
Step 2: This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it using various methods, such as factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring.
Factor the quadratic expression:
(2x - 15)(x + 6) = 0
Step 3: Set each factor equal to zero and solve for x:
2x - 15 = 0 → 2x = 15 → x = 15/2 = 7.5
x + 6 = 0 → x = -6
So, the two possible solutions for x are x = 7.5 and x = -6.
However, since we are looking for a whole number, the only valid solution is x = 7.5.
Therefore, the number is 7.5.