Solve 0 = 4 - 7x^2 x

Question

Solve the equation

x = \frac{3 196}{7}

Alternative Form

x \approx 0.829827

Evaluate

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

Multiply

More Steps

Evaluate

7 x^{2} \times x

Multiply the terms with the same base by adding their exponents

7 x^{2 + 1}

Add the numbers

7 x^{3}

0 = 4 - 7 x^{3}

Swap the sides of the equation

4 - 7 x^{3} = 0

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

- 7 x^{3} = 0 - 4

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

- 7 x^{3} = - 4

Change the signs on both sides of the equation

7 x^{3} = 4

Divide both sides

\frac{7 x ^{3}}{7} = \frac{4}{7}

Divide the numbers

x^{3} = \frac{4}{7}

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

3 x^{3} = 3 \frac{4}{7}

Calculate

x = 3 \frac{4}{7}

Solution

More Steps

Evaluate

3 \frac{4}{7}

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

\frac{3 4}{3 7}

Multiply by the Conjugate

\frac{3 4 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 4 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 349

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

3 4 \times 49

Calculate the product

3196

\frac{3 196}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 196}{7}

x = \frac{3 196}{7}

Alternative Form

x \approx 0.829827

Show Solution