if a number is subtracted twice its reciprocal, the result is -23/5. what is the number?
If you meant: if a number is subtracted from twice its reciprocal , then
2(1/x) - x = -23/5
times x
2 - x^2 = -23/5
times 5
10 - 5x^2 = -23x
5x^2 - 23x - 10 = 0
(x - 5)(5x + 2) = 0
x = 5 or x = -2/5
check:
if x = 5, then 2/5 - 5 = -23/5 , checks!
if x = -2/5), then 2(-5/2) - (-2/5)
= -5 + 2/5
= -23/5 , checks!
It a number is subtracted from twice its reciprocal the result is -23/5 what is the number
Let's assume the number is "x". According to the given information, the equation to represent the problem is:
x - 2(1/x) = -23/5
To solve this equation, we'll start by multiplying each term by 5x to eliminate the fractions:
5x(x) - 5x(2(1/x)) = -23/5(5x)
5x^2 - 10 = -23x
Now, let's rearrange the equation to set it equal to zero:
5x^2 + 23x - 10 = 0
To solve this quadratic equation, we can either factor it, complete the square, or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Here, a = 5, b = 23, and c = -10. Substituting these values into the formula:
x = (-23 ± √(23^2 - 4(5)(-10))) / 2(5)
Simplifying further:
x = (-23 ± √(529 + 200)) / 10
x = (-23 ± √729) / 10
x = (-23 ± 27) / 10
Now, calculating the two possible values for x:
x1 = (-23 + 27) / 10 = 4/10 = 2/5
x2 = (-23 - 27) / 10 = -50 / 10 = -5
Therefore, the two possible solutions for the number are x = 2/5 or x = -5.
To find the number, let's consider the steps:
Let the number be represented by "x".
The reciprocal of x is 1/x.
According to the given information, "a number is subtracted twice its reciprocal, the result is -23/5", we can set up the equation:
x - 2(1/x) = -23/5
To solve this equation, we will proceed as follows:
Step 1: Multiply the entire equation by 5x to eliminate the denominators:
5x(x) - 5x(2)(1/x) = -23/5 * 5x
Simplifying, we get:
5x^2 - 10 = -23x
Step 2: Rearrange the equation to make it a quadratic equation:
5x^2 + 23x - 10 = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0, where:
a = 5
b = 23
c = -10
Step 3: Solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values into the formula:
x = (-23 ± √(23^2 - 4 * 5 * -10)) / (2 * 5)
Simplifying further:
x = (-23 ± √(529 + 200)) / 10
x = (-23 ± √729) / 10
x = (-23 ± 27) / 10
Now, we have two possible solutions:
x1 = (-23 + 27) / 10 = 4 / 10 = 0.4
x2 = (-23 - 27) / 10 = -50 / 10 = -5
Therefore, the two possible values for the number are 0.4 and -5.