Question

Solve using the quadratic formula

100/x+10 + 100/x = 9

Answer 1

To solve the given equation using the quadratic formula, we first need to put the equation in the standard quadratic form: ax^2 + bx + c = 0.

Given equation: 100/x+10 + 100/x = 9

First, let's find a common denominator for the two fractions:
100/x + 100/x = 9
(100(x) + 100(x+10))/(x(x+10)) = 9
(100x + 100(x+10))/(x(x+10)) = 9
(100x + 100x + 1000)/(x(x+10)) = 9
(200x + 1000)/(x(x+10)) = 9

Now, let's multiply both sides by the denominator to eliminate the fraction:
9(x(x+10)) = 200x + 1000
9x^2 + 90x = 200x + 1000
9x^2 + 90x - 200x - 1000 = 0
9x^2 - 110x - 1000 = 0

Now we have the equation in standard quadratic form, so we can apply the quadratic formula. The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation: a = 9, b = -110, c = -1000

x = (-(-110) ± √((-110)^2 - 4(9)(-1000))) / (2(9))
x = (110 ± √(12100 - (-36000))) / 18
x = (110 ± √(48100)) / 18
x = (110 ± 219.37) / 18

Solving for x, we have two possible solutions:
x = (110 + 219.37) / 18
x = 329.37 / 18
x ≈ 18.30

x = (110 - 219.37) / 18
x = -109.37 / 18
x ≈ -6.07

Therefore, the solutions to the given equation are approximately x ≈ 18.30 and x ≈ -6.07.