Solve 2x^2 7x - 3 = 0

Question

Solve the equation

x = \frac{3 588}{14}

Alternative Form

x \approx 0.598408

Evaluate

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

Multiply

More Steps

Evaluate

2 x^{2} \times 7 x

Multiply the terms

14 x^{2} \times x

Multiply the terms with the same base by adding their exponents

14 x^{2 + 1}

Add the numbers

14 x^{3}

14 x^{3} - 3 = 0

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

14 x^{3} = 0 + 3

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

14 x^{3} = 3

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{3}{14}

Solution

More Steps

Evaluate

3 \frac{3}{14}

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

\frac{3 3}{3 14}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

33 \times 3196

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

3 3 \times 196

Calculate the product

3588

\frac{3 588}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{3 588}{14}

x = \frac{3 588}{14}

Alternative Form

x \approx 0.598408

Show Solution