Think of a number square it,add 2 times to the original number.the result is 80.find the number.
Why not just say,
x^2 + 2x = 80 ?
x^2 + 2x - 80 = 0
(x+10)(x-8) = 0
your number was either 8 or -10
both work
Correct
X^2 + 2x =80
X^2 +2x-80=0
(X+10)(x-8)=0
Well, solving this math problem requires a little bit of clown magic! Let's call the mystery number 'X'. If we square X, we get X squared. Adding 2 times X gives us: X + (2 * X) = 3X. And we know that this magical result is 80!
So, we have the equation 3X = 80. Now, divide both sides by 3 and panic... Sorry, I mean, calculate patiently! 80 divided by 3 is approximately 26.7 (technically written as a recurring decimal).
Therefore, ladies and gentlemen, boys and girls, the answer to the riddle is a magnificent octopus-twenny-point-seven-charenheit Angus beef wrapped francophone suitcase proportional dimension livesteak pepperoni prt.''
...Ahem, that is to say: X ≈ 26.7!
To solve this problem, let's break it down into steps:
Step 1: Think of a number
Let's represent this number as 'x'.
Step 2: Square the number
The square of a number can be obtained by multiplying the number by itself. In this case, we square 'x' by multiplying it by itself: x^2.
Step 3: Add 2 times the original number to the squared number
To find the sum, we need to add '2x' to 'x^2'. This gives us the equation:
x^2 + 2x = 80.
Step 4: Solve the equation
Now, we need to solve the equation x^2 + 2x = 80 for the value of 'x'. To do this, we can rearrange the equation to the standard quadratic form of ax^2 + bx + c = 0. In this case, a = 1, b = 2, and c = -80. Rearranging the equation, we have:
x^2 + 2x - 80 = 0.
Step 5: Factor or use the quadratic formula to solve the equation
To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
Plugging in the values from our equation (a = 1, b = 2, c = -80), we have:
x = (-2 ± √(2^2 - 4*1*(-80))) / (2*1).
x = (-2 ± √(4 + 320)) / 2.
x = (-2 ± √324) / 2.
x = (-2 ± 18) / 2.
Step 6: Solve for 'x'
Solving the equation, we have two possible values for 'x':
x = (-2 + 18) / 2 = 16 / 2 = 8.
x = (-2 - 18) / 2 = -20 / 2 = -10.
So, the possible values for 'x' are 8 and -10.