Solve (7x^24x - 2)(x 7)

Question

Simplify the expression

196 x^{4} - 14 x

Evaluate

(7 x^{2} \times 4 x - 2) (x \times 7)

Remove the parentheses

(7 x^{2} \times 4 x - 2) x \times 7

Multiply

More Steps

Multiply the terms

7 x^{2} \times 4 x

Multiply the terms

28 x^{2} \times x

Multiply the terms with the same base by adding their exponents

28 x^{2 + 1}

Add the numbers

28 x^{3}

(28 x^{3} - 2) x \times 7

Use the commutative property to reorder the terms

(28 x^{3} - 2) \times 7 x

Multiply the terms

7 x (28 x^{3} - 2)

Apply the distributive property

7 x \times 28 x^{3} - 7 x \times 2

Multiply the terms

More Steps

Evaluate

7 x \times 28 x^{3}

Multiply the numbers

196 x \times x^{3}

Multiply the terms

More Steps

Evaluate

x \times x^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 3}

Add the numbers

x^{4}

196 x^{4}

196 x^{4} - 7 x \times 2

Solution

196 x^{4} - 14 x

Show Solution

Factor the expression

14 x (14 x^{3} - 1)

Evaluate

(7 x^{2} \times 4 x - 2) (x \times 7)

Remove the parentheses

(7 x^{2} \times 4 x - 2) x \times 7

Multiply

More Steps

Multiply the terms

7 x^{2} \times 4 x

Multiply the terms

28 x^{2} \times x

Multiply the terms with the same base by adding their exponents

28 x^{2 + 1}

Add the numbers

28 x^{3}

(28 x^{3} - 2) x \times 7

Use the commutative property to reorder the terms

(28 x^{3} - 2) \times 7 x

Multiply the terms

7 x (28 x^{3} - 2)

Factor the expression

7 x \times 2 (14 x^{3} - 1)

Solution

14 x (14 x^{3} - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 196}{14}

Alternative Form

x_{1} = 0, x_{2} \approx 0.414913

Evaluate

(7 x^{2} \times 4 x - 2) (x \times 7)

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

(7 x^{2} \times 4 x - 2) (x \times 7) = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 4 x

Multiply the terms

28 x^{2} \times x

Multiply the terms with the same base by adding their exponents

28 x^{2 + 1}

Add the numbers

28 x^{3}

(28 x^{3} - 2) (x \times 7) = 0

Use the commutative property to reorder the terms

(28 x^{3} - 2) \times 7 x = 0

Multiply the terms

7 x (28 x^{3} - 2) = 0

Elimination the left coefficient

x (28 x^{3} - 2) = 0

Separate the equation into 2 possible cases

x = 0 28 x^{3} - 2 = 0

Solve the equation

More Steps

Evaluate

28 x^{3} - 2 = 0

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

28 x^{3} = 0 + 2

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

28 x^{3} = 2

Divide both sides

\frac{28 x ^{3}}{28} = \frac{2}{28}

Divide the numbers

x^{3} = \frac{2}{28}

Cancel out the common factor 2

x^{3} = \frac{1}{14}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{14}

Calculate

x = 3 \frac{1}{14}

Simplify the root

More Steps

Evaluate

3 \frac{1}{14}

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

\frac{3 1}{3 14}

Simplify the radical expression

\frac{1}{3 14}

Multiply by the Conjugate

\frac{3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

\frac{3 196}{14}

x = \frac{3 196}{14}

x = 0 x = \frac{3 196}{14}

Solution

x_{1} = 0, x_{2} = \frac{3 196}{14}

Alternative Form

x_{1} = 0, x_{2} \approx 0.414913

Show Solution