Solve x^(2)-36x^64

Question

Simplify the expression

x^{2} - 144 x^{6}

Evaluate

x^{2} - 36 x^{6} \times 4

Solution

x^{2} - 144 x^{6}

Show Solution

x^{2} (1 - 12 x^{2}) (1 + 12 x^{2})

Evaluate

x^{2} - 36 x^{6} \times 4

Evaluate

x^{2} - 144 x^{6}

Factor out x^{2} from the expression

x^{2} (1 - 144 x^{4})

Solution

More Steps

Evaluate

1 - 144 x^{4}

Rewrite the expression in exponential form

1^{2} - (12 x^{2})^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(1 - 12 x^{2}) (1 + 12 x^{2})

x^{2} (1 - 12 x^{2}) (1 + 12 x^{2})

Show Solution

x_{1} = - \frac{3}{6}, x_{2} = 0, x_{3} = \frac{3}{6}

Alternative Form

x_{1} \approx - 0.288675, x_{2} = 0, x_{3} \approx 0.288675

Evaluate

x^{2} - 36 x^{6} \times 4

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

x^{2} - 36 x^{6} \times 4 = 0

Multiply the terms

x^{2} - 144 x^{6} = 0

Factor the expression

x^{2} (1 - 144 x^{4}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 144 x^{4} = 0

The only way a power can be 0 is when the base equals 0

x = 0 1 - 144 x^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 144 x^{4} = 0

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

- 144 x^{4} = 0 - 1

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

- 144 x^{4} = - 1

Change the signs on both sides of the equation

144 x^{4} = 1

Divide both sides

\frac{144 x ^{4}}{144} = \frac{1}{144}

Divide the numbers

x^{4} = \frac{1}{144}

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

x = \pm 4 \frac{1}{144}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{144}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4 1}{4 144}

Simplify the radical expression

\frac{1}{4 144}

Simplify the radical expression

\frac{1}{2 3}

Multiply by the Conjugate

\frac{3}{2 3 \times 3}

Multiply the numbers

\frac{3}{6}

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

Separate the equation into 2 possible cases

x = \frac{3}{6} x = - \frac{3}{6}

x = 0 x = \frac{3}{6} x = - \frac{3}{6}

Solution

x_{1} = - \frac{3}{6}, x_{2} = 0, x_{3} = \frac{3}{6}

Alternative Form

x_{1} \approx - 0.288675, x_{2} = 0, x_{3} \approx 0.288675

Show Solution