Solve (x^2 -36)2 (x^24x-12)2 =0

Question

Solve the equation

x_{1} = - 6, x_{2} = 33, x_{3} = 6

Alternative Form

x_{1} = - 6, x_{2} \approx 1.44225, x_{3} = 6

Evaluate

(x^{2} - 36) \times 2 (x^{2} \times 4 x - 12) \times 2 = 0

Simplify

More Steps

Evaluate

(x^{2} - 36) \times 2 (x^{2} \times 4 x - 12) \times 2

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

(x^{2} - 36) \times 2 (4 x^{3} - 12) \times 2

Multiply the terms

(x^{2} - 36) \times 4 (4 x^{3} - 12)

Multiply the first two terms

4 (x^{2} - 36) (4 x^{3} - 12)

4 (x^{2} - 36) (4 x^{3} - 12) = 0

Elimination the left coefficient

(x^{2} - 36) (4 x^{3} - 12) = 0

Separate the equation into 2 possible cases

x^{2} - 36 = 0 4 x^{3} - 12 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 36 = 0

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

x^{2} = 0 + 36

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

x^{2} = 36

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

x = \pm 36

Simplify the expression

More Steps

Evaluate

36

Write the number in exponential form with the base of 6

6^{2}

Reduce the index of the radical and exponent with 2

6

x = \pm 6

Separate the equation into 2 possible cases

x = 6 x = - 6

x = 6 x = - 6 4 x^{3} - 12 = 0

Solve the equation

More Steps

Evaluate

4 x^{3} - 12 = 0

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

4 x^{3} = 0 + 12

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

4 x^{3} = 12

Divide both sides

\frac{4 x ^{3}}{4} = \frac{12}{4}

Divide the numbers

x^{3} = \frac{12}{4}

Divide the numbers

More Steps

Evaluate

\frac{12}{4}

Reduce the numbers

\frac{3}{1}

Calculate

3

x^{3} = 3

Take the 3 -th root on both sides of the equation

3 x^{3} = 33

Calculate

x = 33

x = 6 x = - 6 x = 33

Solution

x_{1} = - 6, x_{2} = 33, x_{3} = 6

Alternative Form

x_{1} = - 6, x_{2} \approx 1.44225, x_{3} = 6

Show Solution