Solve 16x-10/x=27

Question

Solve the equation

x_{1} = - \frac{5}{16}, x_{2} = 2

Alternative Form

x_{1} = - 0.3125, x_{2} = 2

Evaluate

16 x - \frac{10}{x} = 27

Find the domain

16 x - \frac{10}{x} = 27, x \neq = 0

Multiply both sides of the equation by LCD

(16 x - \frac{10}{x}) x = 27 x

Simplify the equation

More Steps

Evaluate

(16 x - \frac{10}{x}) x

Apply the distributive property

16 x \times x - \frac{10}{x} \times x

Simplify

16 x \times x - 10

Multiply the terms

16 x^{2} - 10

16 x^{2} - 10 = 27 x

Move the expression to the left side

16 x^{2} - 10 - 27 x = 0

Factor the expression

More Steps

Evaluate

16 x^{2} - 10 - 27 x

Reorder the terms

16 x^{2} - 27 x - 10

Rewrite the expression

16 x^{2} + (5 - 32) x - 10

Calculate

16 x^{2} + 5 x - 32 x - 10

Rewrite the expression

x \times 16 x + x \times 5 - 2 \times 16 x - 2 \times 5

Factor out x from the expression

x (16 x + 5) - 2 \times 16 x - 2 \times 5

Factor out - 2 from the expression

x (16 x + 5) - 2 (16 x + 5)

Factor out 16 x + 5 from the expression

(x - 2) (16 x + 5)

(x - 2) (16 x + 5) = 0

When the product of factors equals 0,at least one factor is 0

x - 2 = 0 16 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

x = 2

x = 2 16 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

16 x + 5 = 0

Move the constant to the right-hand side and change its sign

16 x = 0 - 5

Removing 0 doesn't change the value,so remove it from the expression

16 x = - 5

Divide both sides

\frac{16 x}{16} = \frac{- 5}{16}

Divide the numbers

x = \frac{- 5}{16}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{5}{16}

x = 2 x = - \frac{5}{16}

Check if the solution is in the defined range

x = 2 x = - \frac{5}{16}, x \neq = 0

Find the intersection of the solution and the defined range

x = 2 x = - \frac{5}{16}

Solution

x_{1} = - \frac{5}{16}, x_{2} = 2

Alternative Form

x_{1} = - 0.3125, x_{2} = 2

Show Solution