Solve x^3 4x^2 x-6

Question

Simplify the expression

4 x^{6} - 6

Evaluate

x^{3} \times 4 x^{2} \times x - 6

Solution

More Steps

Evaluate

x^{3} \times 4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

x^{3 + 2 + 1} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 6

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Factor the expression

2 (2 x^{6} - 3)

Evaluate

x^{3} \times 4 x^{2} \times x - 6

Multiply

More Steps

Evaluate

x^{3} \times 4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

x^{3 + 2 + 1} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 6

Solution

2 (2 x^{6} - 3)

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Find the roots

x_{1} = - \frac{6 96}{2}, x_{2} = \frac{6 96}{2}

Alternative Form

x_{1} \approx - 1.069913, x_{2} \approx 1.069913

Evaluate

x^{3} \times 4 x^{2} \times x - 6

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

x^{3} \times 4 x^{2} \times x - 6 = 0

Multiply

More Steps

Multiply the terms

x^{3} \times 4 x^{2} \times x

Multiply the terms with the same base by adding their exponents

x^{3 + 2 + 1} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 6 = 0

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

4 x^{6} = 0 + 6

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

4 x^{6} = 6

Divide both sides

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

Divide the numbers

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

Cancel out the common factor 2

x^{6} = \frac{3}{2}

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

x = \pm 6 \frac{3}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{3}{2}

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

\frac{6 3}{6 2}

Multiply by the Conjugate

\frac{6 3 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 3 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

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Evaluate

63 \times 632

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

6 3 \times 32

Calculate the product

696

\frac{6 96}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

62 \times 6 2^{5}

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

6 2 \times 2^{5}

Calculate the product

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{6 96}{2}

x = \pm \frac{6 96}{2}

Separate the equation into 2 possible cases

x = \frac{6 96}{2} x = - \frac{6 96}{2}

Solution

x_{1} = - \frac{6 96}{2}, x_{2} = \frac{6 96}{2}

Alternative Form

x_{1} \approx - 1.069913, x_{2} \approx 1.069913

Show Solution