Solve 3x^2 - 24x^48

Question

Simplify the expression

3 x^{2} - 192 x^{4}

Evaluate

3 x^{2} - 24 x^{4} \times 8

Solution

3 x^{2} - 192 x^{4}

Show Solution

3 x^{2} (1 - 8 x) (1 + 8 x)

Evaluate

3 x^{2} - 24 x^{4} \times 8

Evaluate

3 x^{2} - 192 x^{4}

Factor out 3 x^{2} from the expression

3 x^{2} (1 - 64 x^{2})

Solution

More Steps

Evaluate

1 - 64 x^{2}

Rewrite the expression in exponential form

1^{2} - (8 x)^{2}

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

(1 - 8 x) (1 + 8 x)

3 x^{2} (1 - 8 x) (1 + 8 x)

Show Solution

x_{1} = - \frac{1}{8}, x_{2} = 0, x_{3} = \frac{1}{8}

Alternative Form

x_{1} = - 0.125, x_{2} = 0, x_{3} = 0.125

Evaluate

3 x^{2} - 24 x^{4} \times 8

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

3 x^{2} - 24 x^{4} \times 8 = 0

Multiply the terms

3 x^{2} - 192 x^{4} = 0

Factor the expression

3 x^{2} (1 - 64 x^{2}) = 0

Divide both sides

x^{2} (1 - 64 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 64 x^{2} = 0

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

x = 0 1 - 64 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 64 x^{2} = 0

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

- 64 x^{2} = 0 - 1

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

- 64 x^{2} = - 1

Change the signs on both sides of the equation

64 x^{2} = 1

Divide both sides

\frac{64 x ^{2}}{64} = \frac{1}{64}

Divide the numbers

x^{2} = \frac{1}{64}

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

x = \pm \frac{1}{64}

Simplify the expression

More Steps

Evaluate

\frac{1}{64}

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

\frac{1}{64}

Simplify the radical expression

\frac{1}{64}

Simplify the radical expression

\frac{1}{8}

x = \pm \frac{1}{8}

Separate the equation into 2 possible cases

x = \frac{1}{8} x = - \frac{1}{8}

x = 0 x = \frac{1}{8} x = - \frac{1}{8}

Solution

x_{1} = - \frac{1}{8}, x_{2} = 0, x_{3} = \frac{1}{8}

Alternative Form

x_{1} = - 0.125, x_{2} = 0, x_{3} = 0.125

Show Solution