Solve 2x^(2) 4x-1

Question

Simplify the expression

8 x^{3} - 1

Evaluate

2 x^{2} \times 4 x - 1

Solution

More Steps

Evaluate

2 x^{2} \times 4 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

8 x^{3} - 1

Show Solution

Factor the expression

(2 x - 1) (4 x^{2} + 2 x + 1)

Evaluate

2 x^{2} \times 4 x - 1

Evaluate

More Steps

Evaluate

2 x^{2} \times 4 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

8 x^{3} - 1

Rewrite the expression in exponential form

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

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(2 x - 1) ((2 x)^{2} + 2 x \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(2 x)^{2}

To raise a product to a power,raise each factor to that power

2^{2} x^{2}

Evaluate the power

4 x^{2}

(2 x - 1) (4 x^{2} + 2 x \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(2 x - 1) (4 x^{2} + 2 x + 1^{2})

Solution

(2 x - 1) (4 x^{2} + 2 x + 1)

Show Solution

Find the roots

x = \frac{1}{2}

Alternative Form

x = 0.5

Evaluate

2 x^{2} \times 4 x - 1

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

2 x^{2} \times 4 x - 1 = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times 4 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

8 x^{3} - 1 = 0

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

8 x^{3} = 0 + 1

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

8 x^{3} = 1

Divide both sides

\frac{8 x ^{3}}{8} = \frac{1}{8}

Divide the numbers

x^{3} = \frac{1}{8}

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

3 x^{3} = 3 \frac{1}{8}

Calculate

x = 3 \frac{1}{8}

Solution

More Steps

Evaluate

3 \frac{1}{8}

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

\frac{3 1}{3 8}

Simplify the radical expression

\frac{1}{3 8}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{1}{2}

x = \frac{1}{2}

Alternative Form

x = 0.5

Show Solution