Solve 6-24x^44 - ScanMath

Question

Simplify the expression

6 - 96 x^{4}

Evaluate

6 - 24 x^{4} \times 4

Solution

6 - 96 x^{4}

Show Solution

6 (1 - 2 x) (1 + 2 x) (1 + 4 x^{2})

Evaluate

6 - 24 x^{4} \times 4

Evaluate

6 - 96 x^{4}

Factor out 6 from the expression

6 (1 - 16 x^{4})

Factor the expression

More Steps

Evaluate

1 - 16 x^{4}

Rewrite the expression in exponential form

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

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

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

6 (1 - 4 x^{2}) (1 + 4 x^{2})

Solution

More Steps

Evaluate

1 - 4 x^{2}

Rewrite the expression in exponential form

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

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

(1 - 2 x) (1 + 2 x)

6 (1 - 2 x) (1 + 2 x) (1 + 4 x^{2})

Show Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0.5

Evaluate

6 - 24 x^{4} \times 4

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

6 - 24 x^{4} \times 4 = 0

Multiply the terms

6 - 96 x^{4} = 0

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

- 96 x^{4} = 0 - 6

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

- 96 x^{4} = - 6

Change the signs on both sides of the equation

96 x^{4} = 6

Divide both sides

\frac{96 x ^{4}}{96} = \frac{6}{96}

Divide the numbers

x^{4} = \frac{6}{96}

Cancel out the common factor 6

x^{4} = \frac{1}{16}

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

x = \pm 4 \frac{1}{16}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{16}

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

\frac{4 1}{4 16}

Simplify the radical expression

\frac{1}{4 16}

Simplify the radical expression

More Steps

Evaluate

416

Write the number in exponential form with the base of 2

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{1}{2}

x = \pm \frac{1}{2}

Separate the equation into 2 possible cases

x = \frac{1}{2} x = - \frac{1}{2}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0.5

Show Solution