Solve for x
1/x+1/(x+16)=1/15
I think I finally got this one
x=24, x=-10
correct?
correct.
Just plug in the values of x to check if those value are correct!
To solve for x in the equation:
1/x + 1/(x + 16) = 1/15
We need to get rid of the denominators by finding a common denominator. In this case, the common denominator is 15x(x + 16).
Multiplying both sides of the equation by 15x(x + 16) will eliminate the fractions:
15(x + 16) + 15x = x(x + 16)
Expanding the brackets:
15x + 240 + 15x = x^2 + 16x
Combining like terms:
30x + 240 = x^2 + 16x
Rearranging the equation:
x^2 + 16x - 30x - 240 = 0
Simplifying:
x^2 - 14x - 240 = 0
Now, we can solve this quadratic equation. We can factor this equation or use 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 = -14, and c = -240. Substituting these values into the quadratic formula:
x = (14 ± √((-14)^2 - 4(1)(-240)))/(2(1))
Simplifying:
x = (14 ± √(196 + 960))/2
x = (14 ± √1156)/2
x = (14 ± 34)/2
Now, we have two possible solutions:
x1 = (14 + 34)/2 = 48/2 = 24
x2 = (14 - 34)/2 = -20/2 = -10
Hence, the solutions for x in the equation are x = 24 and x = -10.