x 10
- + - = 7
1 x
I don't think anyone will understand what you are looking for.
re-write
x/1 + 10/x =7
x/1 + 10/x =7
multiply both sides by x
x^2 + 10 = 7x
x^2 - 7x + 10 = 0
(x - 5)(x - 2) = 0
x = 5, x = 2
To solve the equation "x/10 - 1/x = 7", you need to isolate the variable x on one side of the equation. Here's how you can proceed:
Step 1: Multiply the entire equation by 10x to eliminate the fractions.
(x/10) * 10x - (1/x) * 10x = 7 * 10x
Simplifying the above equation gives:
x^2 - 10 = 70x
Step 2: Rearrange the equation to form a quadratic equation in standard form.
x^2 - 70x - 10 = 0
Step 3: Solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, factoring or completing the square may not be efficient methods, so let's use the quadratic formula:
For an equation in the form ax^2 + bx + c = 0, the quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Comparing the quadratic equation with the standard form, we have:
a = 1, b = -70, c = -10
Substituting these values into the quadratic formula, we get:
x = (-(-70) ± sqrt((-70)^2 - 4(1)(-10))) / (2 * 1)
Simplifying further gives:
x = (70 ± sqrt(4900 + 40)) / 2
x = (70 ± sqrt(4940)) / 2
Now we need to calculate the square root of 4940:
sqrt(4940) ≈ 70.29
Substituting this value back into the formula, we get two possible solutions:
x₁ = (70 + 70.29) / 2 ≈ 70.15
x₂ = (70 - 70.29) / 2 ≈ -0.15
Therefore, the solutions to the equation "x/10 - 1/x = 7" are approximately x ≈ 70.15 and x ≈ -0.15.