Solve 4x^27x-1/2=0

Question

Solve the equation

x = \frac{3 49}{14}

Alternative Form

x \approx 0.261379

Evaluate

4 x^{2} \times 7 x - \frac{1}{2} = 0

Multiply

More Steps

Evaluate

4 x^{2} \times 7 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} - \frac{1}{2} = 0

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

28 x^{3} = 0 + \frac{1}{2}

Add the terms

28 x^{3} = \frac{1}{2}

Multiply by the reciprocal

28 x^{3} \times \frac{1}{28} = \frac{1}{2} \times \frac{1}{28}

Multiply

x^{3} = \frac{1}{2} \times \frac{1}{28}

Multiply

More Steps

Evaluate

\frac{1}{2} \times \frac{1}{28}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{2 \times 28}

Multiply the numbers

\frac{1}{56}

x^{3} = \frac{1}{56}

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

3 x^{3} = 3 \frac{1}{56}

Calculate

x = 3 \frac{1}{56}

Solution

More Steps

Evaluate

3 \frac{1}{56}

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

\frac{3 1}{3 56}

Simplify the radical expression

\frac{1}{3 56}

Simplify the radical expression

More Steps

Evaluate

356

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 7

Write the number in exponential form with the base of 2

3 2^{3} \times 7

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 37

Reduce the index of the radical and exponent with 3

237

\frac{1}{2 3 7}

Multiply by the Conjugate

\frac{3 7 ^{2}}{2 3 7 \times 3 7 ^{2}}

Simplify

\frac{3 49}{2 3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

237 \times 3 7^{2}

Multiply the terms

2 \times 7

Multiply the terms

14

\frac{3 49}{14}

x = \frac{3 49}{14}

Alternative Form

x \approx 0.261379

Show Solution