Solve sqrt(x^3 12x^2 36x-162)

Question

Simplify the expression

3 48 x^{6} - 18

Show Solution

x_{1} = - \frac{6 24}{2}, x_{2} = \frac{6 24}{2}

Alternative Form

x_{1} \approx - 0.849191, x_{2} \approx 0.849191

Evaluate

x^{3} \times 12 x^{2} \times 36 x - 162

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

x^{3} \times 12 x^{2} \times 36 x - 162 = 0

Find the domain

More Steps

x^{3} \times 12 x^{2} \times 36 x - 162 = 0, x \in (- \infty, - \frac{6 24}{2}] \cup [\frac{6 24}{2}, + \infty)

Calculate

x^{3} \times 12 x^{2} \times 36 x - 162 = 0

Multiply

More Steps

432 x^{6} - 162 = 0

Simplify the root

More Steps

3 48 x^{6} - 18 = 0

Rewrite the expression

48 x^{6} - 18 = 0

The only way a root could be 0 is when the radicand equals 0

48 x^{6} - 18 = 0

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

48 x^{6} = 0 + 18

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

48 x^{6} = 18

Divide both sides

\frac{48 x ^{6}}{48} = \frac{18}{48}

Divide the numbers

x^{6} = \frac{18}{48}

Cancel out the common factor 6

x^{6} = \frac{3}{8}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{3}{8}

Simplify the expression

More Steps

x = \pm \frac{6 24}{2}

Separate the equation into 2 possible cases

x = \frac{6 24}{2} x = - \frac{6 24}{2}

Check if the solution is in the defined range

x = \frac{6 24}{2} x = - \frac{6 24}{2}, x \in (- \infty, - \frac{6 24}{2}] \cup [\frac{6 24}{2}, + \infty)

Find the intersection of the solution and the defined range

x = \frac{6 24}{2} x = - \frac{6 24}{2}

Solution

x_{1} = - \frac{6 24}{2}, x_{2} = \frac{6 24}{2}

Alternative Form

x_{1} \approx - 0.849191, x_{2} \approx 0.849191

Show Solution