The square of a certain number is 22cm than 13 time the original number find the number
x is 11 or 2
Let's assume the original number is "x".
According to the given information, the square of this number is 22 less than 13 times the original number. We can write this equation:
x^2 = 13x - 22
To find the value of x, we need to solve this quadratic equation. Let's rearrange it:
x^2 - 13x + 22 = 0
Now, we can solve this equation by factorizing, completing the square, or using the quadratic formula. Let's use the quadratic formula:
The quadratic formula states that for an equation ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x=(-b±√(b^2-4ac))/(2a)
In our equation, a=1, b=-13, and c=22. Plugging in these values into the quadratic formula:
x = (-(-13) ± √((-13)^2 - 4*1*22))/(2*1)
= (13 ± √(169 - 88))/(2)
= (13 ± √81)/(2)
Simplifying further:
x = (13 ± 9)/(2)
We get two possible solutions:
1. x = (13 + 9)/(2)
x = 22/2
x = 11
2. x = (13 - 9)/(2)
x = 4/2
x = 2
Therefore, the possible values for the number "x" are 11 and 2.
To find the number, let's set up an equation.
Let's assume the original number is "x."
According to the problem, the square of the number is 22 more than 13 times the original number. So, we can write this as an equation:
x^2 = 13x + 22
To solve this equation, we need to rearrange it into a quadratic equation by moving all terms to one side:
x^2 - 13x - 22 = 0
Now, we can solve this quadratic equation in two ways - factoring or using the quadratic formula. Let's use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 1, b = -13, and c = -22.
Plugging in these values into the quadratic formula, we get:
x = (-(-13) ± √((-13)^2 - 4(1)(-22))) / (2 * 1)
Simplifying further:
x = (13 ± √(169 + 88)) / 2
x = (13 ± √257) / 2
Now, taking the positive and negative square roots of 257:
x = (13 + √257) / 2 ≈ 11.94
or
x = (13 - √257) / 2 ≈ 1.06
So, the two possible solutions for the number are approximately 11.94 and 1.06.
x^2 = 13x-22
Now solve for x.