I think of a number square it and add 2 times the original number.the resuit is 80.find the number
n^2 + 2 n = 80 ... n^2 + 2 n - 80 = 0
factoring ... (n + 10) (n - 8) = 0
n + 10 = 0 ... n = -10
n - 8 = 0 ... n = 8
X^2 + 2x =80
X^2 +2x-80=0
(X+10)(x-8)=0
Well, well, well, let me put on my math clown hat for this one!
If we read the problem carefully, it says to square a number, add twice the original number, and the result is 80. So, let me break it down with some laughter!
Let's say our mysterious number is "x". We square it, which gives us x^2. Then we add 2 times the original number, which is 2x. And voila, the magical equation appears:
x^2 + 2x = 80
Now, to solve this, we can bring all the terms to one side:
x^2 + 2x - 80 = 0
Alright, now we have a nice quadratic equation. But fear not, we shall find the answer with a smile on our faces! Using some clown magic (also known as factoring or the quadratic formula), we get:
(x + 10)(x - 8) = 0
Now, if we set each factor equal to zero, we find two possible values for our mysterious number:
x + 10 = 0 or x - 8 = 0
Solving these equations, we find:
x = -10 or x = 8
Ta-da! We have discovered two possible numbers that satisfy the given conditions. So, the answer could be either -10 or 8. Choose wisely, my friend, and keep laughing along the way!
Let's solve the problem step-by-step:
Let's assume the original number is "x".
Step 1: Square the number
x^2
Step 2: Add 2 times the original number
x^2 + 2x
Step 3: Set it equal to 80
x^2 + 2x = 80
Now, we have a quadratic equation. Let's solve it by rearranging it to the standard form:
x^2 + 2x - 80 = 0
Now we can factor the quadratic equation:
(x + 10)(x - 8) = 0
Now, we can set each factor equal to zero and solve for "x":
x + 10 = 0 or x - 8 = 0
Solving for "x" in both equations:
x = -10 or x = 8
However, since we're looking for a number, it cannot be negative in this case. So, the number is:
x = 8
Therefore, the number is 8.
To solve this problem, we can start by translating the given information into an equation.
Let's say the number you are thinking of is "x".
According to the problem, you square the number and add 2 times the original number, resulting in 80. Mathematically, this can be represented as:
x^2 + 2x = 80
Now, we have a quadratic equation. To solve it, we need to rearrange it into the standard quadratic form, which is:
x^2 + 2x - 80 = 0
To find the value of "x" that satisfies this equation, we can either factor the quadratic equation or use the quadratic formula.
Let's solve it using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 2, and c = -80.
Substituting the values into the quadratic formula, we can now calculate "x":
x = (-2 ± √(2^2 - 4(1)(-80))) / (2(1))
x = (-2 ± √(4 + 320)) / 2
x = (-2 ± √324) / 2
x = (-2 ± 18) / 2
Simplifying further:
x = (-2 + 18) / 2 or x = (-2 - 18) / 2
x1 = 16/2 = 8
x2 = -20/2 = -10
Therefore, the possible solutions for "x" are x = 8 and x = -10.