If 13 Times A Number Is Subtracted From The Square Of The Number,the Result Is 30.Find The Number.
x^2 - 13x = 30
x^2 - 13x - 30 = 0
(x-15)(x+2) = 0
can you take over ?
(x-15)=0 OR (x+2)=0
x=15 or x=-2
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Well, if we let the number be x, we can set up the equation x^2 - 13x = 30. But let's not get too squared away with this problem! Let's give this equation a little break and have some fun with it.
So let's imagine this equation as a playground, where x is the number having a fantastic time on the swings. Now, imagine 13 times x coming along, trying to ruin the fun by subtracting it. But x is smart, and it knows that math problems are no match for swings, so it decides to square itself to deal with the troublemaker.
And what does it get after squaring itself? Well, it gets 30, which is basically the ultimate slide at the playground! So the number x is not only having a grand old time on the swings but also enjoying a thrilling slide adventure.
Now, let's find out what number is a math playground champion. By rearranging the equation, we get x^2 - 13x - 30 = 0. Factoring this gives us (x - 15)(x + 2) = 0. So, either x - 15 = 0 or x + 2 = 0.
If x - 15 = 0, then x = 15. And if x + 2 = 0, then x = -2. So, the number that solves the equation is either 15 or -2.
Now, let's imagine those numbers on the math playground. 15 is the popular kid, swinging high and enjoying life, while -2 is the mischievous trickster, swinging upside down and making everyone laugh.
In conclusion, the number could be either 15 or -2. Let's just hope they leave the math playground in one piece!
To find the number, let's use algebra.
Let's assume the number is represented by the variable 'x'.
According to the problem, "13 times a number is subtracted from the square of the number, the result is 30." So we can write this in an equation as:
x^2 - 13x = 30
To solve this equation, we need to bring all terms to one side of the equation and set it equal to zero:
x^2 - 13x - 30 = 0
Now we have a quadratic equation that we can factor or solve using the quadratic formula. Let's factor it:
(x - 15)(x + 2) = 0
Setting each factor equal to zero:
x - 15 = 0 or x + 2 = 0
Solving for 'x' in each case:
x = 15 or x = -2
So the two possible answers for the number are 15 and -2.