solve the equation below algebraically and express the result in simplest radical form
13/x=10-x
I did 13/x=10-x
multiplied each side by x and then subtracted 13 to get
0=13-(10x-x^2)
x^2-10x+13=0
x=(10+/- square root of 100-52)/2
x=(10=/- 4square root 3) /2
my answer was x=5+/- 2square root 3
was this right? thank you
yes, I simply used my calculator and subbed your answer
It worked.
Thank you
you're welcome
Yes, your solution is correct. Let's go through the steps to solve the equation algebraically and express the result in simplest radical form:
1. Start with the equation: 13/x = 10 - x.
2. Multiply both sides of the equation by x to eliminate fractions:
(13/x) * x = (10 - x) * x
=> 13 = 10x - x^2
3. Rearrange the equation to form a quadratic equation in standard form:
x^2 - 10x + 13 = 0
4. To factorize or solve the quadratic equation, we apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing to our equation, a = 1, b = -10, and c = 13.
5. Substitute these values into the quadratic formula:
x = (-( -10) ± √((-10)^2 - 4(1)(13))) / (2(1))
= ( 10 ± √(100 - 52)) / 2
= ( 10 ± √48) / 2
= ( 10 ± √(16 * 3)) / 2
= ( 10 ± 4√3) / 2
6. Simplify further by dividing both terms by 2:
x = 10/2 ± (4√3)/2
= 5 ± 2√3
So, your answer x = 5 ± 2√3 is correct.