Solve x^2 2x \sqrt x^2 2x 8 -12 = 0

Question

Solve the equation

x = \frac{5 12}{2}

Alternative Form

x \approx 0.821876

Evaluate

x^{2} \times 2 x (x)^{2} \times 2 x \times 8 - 12 = 0

Find the domain

x^{2} \times 2 x (x)^{2} \times 2 x \times 8 - 12 = 0, x \geq 0

Multiply

More Steps

32 x^{5} - 12 = 0

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

32 x^{5} = 0 + 12

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

32 x^{5} = 12

Divide both sides

\frac{32 x ^{5}}{32} = \frac{12}{32}

Divide the numbers

x^{5} = \frac{12}{32}

Cancel out the common factor 4

x^{5} = \frac{3}{8}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{3}{8}

Calculate

x = 5 \frac{3}{8}

Simplify the root

More Steps

x = \frac{5 12}{2}

Check if the solution is in the defined range

x = \frac{5 12}{2}, x \geq 0

Find the intersection of the solution and the defined range

x = \frac{5 12}{2}

Solution

More Steps

x = \frac{5 12}{2}

Alternative Form

x \approx 0.821876

Show Solution