Solve 5x^34x^3-2 - ScanMath

Question

Simplify the expression

20 x^{6} - 2

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms

20 x^{3} \times x^{3}

Multiply the terms with the same base by adding their exponents

20 x^{3 + 3}

Add the numbers

20 x^{6}

20 x^{6} - 2

Show Solution

Factor the expression

2 (10 x^{6} - 1)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

20 x^{3} \times x^{3}

Multiply the terms with the same base by adding their exponents

20 x^{3 + 3}

Add the numbers

20 x^{6}

20 x^{6} - 2

Solution

2 (10 x^{6} - 1)

Show Solution

Find the roots

x_{1} = - \frac{6 1 0 ^{5}}{10}, x_{2} = \frac{6 1 0 ^{5}}{10}

Alternative Form

x_{1} \approx - 0.681292, x_{2} \approx 0.681292

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

20 x^{3} \times x^{3}

Multiply the terms with the same base by adding their exponents

20 x^{3 + 3}

Add the numbers

20 x^{6}

20 x^{6} - 2 = 0

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

20 x^{6} = 0 + 2

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

20 x^{6} = 2

Divide both sides

\frac{20 x ^{6}}{20} = \frac{2}{20}

Divide the numbers

x^{6} = \frac{2}{20}

Cancel out the common factor 2

x^{6} = \frac{1}{10}

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

x = \pm 6 \frac{1}{10}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{10}

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

\frac{6 1}{6 10}

Simplify the radical expression

\frac{1}{6 10}

Multiply by the Conjugate

\frac{6 1 0 ^{5}}{6 10 \times 6 1 0 ^{5}}

Multiply the numbers

More Steps

Evaluate

610 \times 6 1 0^{5}

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

6 10 \times 1 0^{5}

Calculate the product

6 1 0^{6}

Reduce the index of the radical and exponent with 6

10

\frac{6 1 0 ^{5}}{10}

x = \pm \frac{6 1 0 ^{5}}{10}

Separate the equation into 2 possible cases

x = \frac{6 1 0 ^{5}}{10} x = - \frac{6 1 0 ^{5}}{10}

Solution

x_{1} = - \frac{6 1 0 ^{5}}{10}, x_{2} = \frac{6 1 0 ^{5}}{10}

Alternative Form

x_{1} \approx - 0.681292, x_{2} \approx 0.681292

Show Solution