Solve 14-3x^2x^2 9709

Question

Simplify the expression

14 - 29127 x^{4}

Evaluate

14 - 3 x^{2} \times x^{2} \times 9709

Solution

More Steps

Evaluate

3 x^{2} \times x^{2} \times 9709

Multiply the terms

29127 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

29127 x^{2 + 2}

Add the numbers

29127 x^{4}

14 - 29127 x^{4}

Show Solution

Factor the expression

7 (2 - 4161 x^{4})

Evaluate

14 - 3 x^{2} \times x^{2} \times 9709

Multiply

More Steps

Evaluate

3 x^{2} \times x^{2} \times 9709

Multiply the terms

29127 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

29127 x^{2 + 2}

Add the numbers

29127 x^{4}

14 - 29127 x^{4}

Solution

7 (2 - 4161 x^{4})

Show Solution

Find the roots

x_{1} = - \frac{4 2 \times 416 1 ^{3}}{4161}, x_{2} = \frac{4 2 \times 416 1 ^{3}}{4161}

Alternative Form

x_{1} \approx - 0.148067, x_{2} \approx 0.148067

Evaluate

14 - 3 x^{2} \times x^{2} \times 9709

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

14 - 3 x^{2} \times x^{2} \times 9709 = 0

Multiply

More Steps

Multiply the terms

3 x^{2} \times x^{2} \times 9709

Multiply the terms

29127 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

29127 x^{2 + 2}

Add the numbers

29127 x^{4}

14 - 29127 x^{4} = 0

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

- 29127 x^{4} = 0 - 14

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

- 29127 x^{4} = - 14

Change the signs on both sides of the equation

29127 x^{4} = 14

Divide both sides

\frac{29127 x ^{4}}{29127} = \frac{14}{29127}

Divide the numbers

x^{4} = \frac{14}{29127}

Cancel out the common factor 7

x^{4} = \frac{2}{4161}

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

x = \pm 4 \frac{2}{4161}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{4161}

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

\frac{4 2}{4 4161}

Multiply by the Conjugate

\frac{4 2 \times 4 416 1 ^{3}}{4 4161 \times 4 416 1 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 2 \times 416 1 ^{3}}{4 4161 \times 4 416 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

44161 \times 4 416 1^{3}

The product of roots with the same index is equal to the root of the product

4 4161 \times 416 1^{3}

Calculate the product

4 416 1^{4}

Reduce the index of the radical and exponent with 4

4161

\frac{4 2 \times 416 1 ^{3}}{4161}

x = \pm \frac{4 2 \times 416 1 ^{3}}{4161}

Separate the equation into 2 possible cases

x = \frac{4 2 \times 416 1 ^{3}}{4161} x = - \frac{4 2 \times 416 1 ^{3}}{4161}

Solution

x_{1} = - \frac{4 2 \times 416 1 ^{3}}{4161}, x_{2} = \frac{4 2 \times 416 1 ^{3}}{4161}

Alternative Form

x_{1} \approx - 0.148067, x_{2} \approx 0.148067

Show Solution