Solve 7-4x^4x 83x

Question

Simplify the expression

7 - 332 x^{6}

Evaluate

7 - 4 x^{4} \times x \times 83 x

Solution

More Steps

Evaluate

4 x^{4} \times x \times 83 x

Multiply the terms

332 x^{4} \times x \times x

Multiply the terms with the same base by adding their exponents

332 x^{4 + 1 + 1}

Add the numbers

332 x^{6}

7 - 332 x^{6}

Show Solution

x_{1} = - \frac{6 7 \times 33 2 ^{5}}{332}, x_{2} = \frac{6 7 \times 33 2 ^{5}}{332}

Alternative Form

x_{1} \approx - 0.525606, x_{2} \approx 0.525606

Evaluate

7 - 4 x^{4} \times x \times 83 x

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

7 - 4 x^{4} \times x \times 83 x = 0

Multiply

More Steps

Multiply the terms

4 x^{4} \times x \times 83 x

Multiply the terms

332 x^{4} \times x \times x

Multiply the terms with the same base by adding their exponents

332 x^{4 + 1 + 1}

Add the numbers

332 x^{6}

7 - 332 x^{6} = 0

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

- 332 x^{6} = 0 - 7

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

- 332 x^{6} = - 7

Change the signs on both sides of the equation

332 x^{6} = 7

Divide both sides

\frac{332 x ^{6}}{332} = \frac{7}{332}

Divide the numbers

x^{6} = \frac{7}{332}

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

x = \pm 6 \frac{7}{332}

Simplify the expression

More Steps

Evaluate

6 \frac{7}{332}

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

\frac{6 7}{6 332}

Multiply by the Conjugate

\frac{6 7 \times 6 33 2 ^{5}}{6 332 \times 6 33 2 ^{5}}

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

\frac{6 7 \times 33 2 ^{5}}{6 332 \times 6 33 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

6332 \times 6 33 2^{5}

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

6 332 \times 33 2^{5}

Calculate the product

6 33 2^{6}

Reduce the index of the radical and exponent with 6

332

\frac{6 7 \times 33 2 ^{5}}{332}

x = \pm \frac{6 7 \times 33 2 ^{5}}{332}

Separate the equation into 2 possible cases

x = \frac{6 7 \times 33 2 ^{5}}{332} x = - \frac{6 7 \times 33 2 ^{5}}{332}

Solution

x_{1} = - \frac{6 7 \times 33 2 ^{5}}{332}, x_{2} = \frac{6 7 \times 33 2 ^{5}}{332}

Alternative Form

x_{1} \approx - 0.525606, x_{2} \approx 0.525606

Show Solution