Solve 3x^3 14x^2 13x-6

Question

Simplify the expression

546 x^{6} - 6

Evaluate

3 x^{3} \times 14 x^{2} \times 13 x - 6

Solution

More Steps

Evaluate

3 x^{3} \times 14 x^{2} \times 13 x

Multiply the terms

More Steps

Evaluate

3 \times 14 \times 13

Multiply the terms

42 \times 13

Multiply the numbers

546

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

Multiply the terms with the same base by adding their exponents

546 x^{3 + 2 + 1}

Add the numbers

546 x^{6}

546 x^{6} - 6

Show Solution

Factor the expression

6 (91 x^{6} - 1)

Evaluate

3 x^{3} \times 14 x^{2} \times 13 x - 6

Multiply

More Steps

Evaluate

3 x^{3} \times 14 x^{2} \times 13 x

Multiply the terms

More Steps

Evaluate

3 \times 14 \times 13

Multiply the terms

42 \times 13

Multiply the numbers

546

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

Multiply the terms with the same base by adding their exponents

546 x^{3 + 2 + 1}

Add the numbers

546 x^{6}

546 x^{6} - 6

Solution

6 (91 x^{6} - 1)

Show Solution

Find the roots

x_{1} = - \frac{6 9 1 ^{5}}{91}, x_{2} = \frac{6 9 1 ^{5}}{91}

Alternative Form

x_{1} \approx - 0.471512, x_{2} \approx 0.471512

Evaluate

3 x^{3} \times 14 x^{2} \times 13 x - 6

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

3 x^{3} \times 14 x^{2} \times 13 x - 6 = 0

Multiply

More Steps

Multiply the terms

3 x^{3} \times 14 x^{2} \times 13 x

Multiply the terms

More Steps

Evaluate

3 \times 14 \times 13

Multiply the terms

42 \times 13

Multiply the numbers

546

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

Multiply the terms with the same base by adding their exponents

546 x^{3 + 2 + 1}

Add the numbers

546 x^{6}

546 x^{6} - 6 = 0

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

546 x^{6} = 0 + 6

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

546 x^{6} = 6

Divide both sides

\frac{546 x ^{6}}{546} = \frac{6}{546}

Divide the numbers

x^{6} = \frac{6}{546}

Cancel out the common factor 6

x^{6} = \frac{1}{91}

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

x = \pm 6 \frac{1}{91}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{91}

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

\frac{6 1}{6 91}

Simplify the radical expression

\frac{1}{6 91}

Multiply by the Conjugate

\frac{6 9 1 ^{5}}{6 91 \times 6 9 1 ^{5}}

Multiply the numbers

More Steps

Evaluate

691 \times 6 9 1^{5}

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

6 91 \times 9 1^{5}

Calculate the product

6 9 1^{6}

Reduce the index of the radical and exponent with 6

91

\frac{6 9 1 ^{5}}{91}

x = \pm \frac{6 9 1 ^{5}}{91}

Separate the equation into 2 possible cases

x = \frac{6 9 1 ^{5}}{91} x = - \frac{6 9 1 ^{5}}{91}

Solution

x_{1} = - \frac{6 9 1 ^{5}}{91}, x_{2} = \frac{6 9 1 ^{5}}{91}

Alternative Form

x_{1} \approx - 0.471512, x_{2} \approx 0.471512

Show Solution