Solve x-8 * sqrt(x-8)

Question

Find the roots

x_{1} = 32 - 162, x_{2} = 32 + 162

Alternative Form

x_{1} \approx 9.372583, x_{2} \approx 54.627417

Evaluate

x - 8 x - 8

To find the roots of the expression,set the expression equal to 0

x - 8 x - 8 = 0

Find the domain

More Steps

x - 8 x - 8 = 0, x \geq 8

Calculate

x - 8 x - 8 = 0

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

- 8 x - 8 = - x

Divide both sides of the equation by - 1

8 x - 8 = x

Rewrite the expression

x - 8 = \frac{x}{8}

Evaluate

x - 8 = \frac{x}{8}, \frac{x}{8} \geq 0

Evaluate

x - 8 = \frac{x}{8}, x \geq 0

Solve the equation for x

More Steps

x = 32 + 162 x = 32 - 162, x \geq 0

Find the intersection

x = 32 + 162 x = 32 - 162

Check if the solution is in the defined range

x = 32 + 162 x = 32 - 162, x \geq 8

Find the intersection of the solution and the defined range

x = 32 + 162 x = 32 - 162

Solution

x_{1} = 32 - 162, x_{2} = 32 + 162

Alternative Form

x_{1} \approx 9.372583, x_{2} \approx 54.627417

Show Solution