Solve 2x^2 17x-307=0

Question

Solve the equation

x = \frac{3 354892}{34}

Alternative Form

x \approx 2.082347

Evaluate

2 x^{2} \times 17 x - 307 = 0

Multiply

More Steps

Evaluate

2 x^{2} \times 17 x

Multiply the terms

34 x^{2} \times x

Multiply the terms with the same base by adding their exponents

34 x^{2 + 1}

Add the numbers

34 x^{3}

34 x^{3} - 307 = 0

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

34 x^{3} = 0 + 307

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

34 x^{3} = 307

Divide both sides

\frac{34 x ^{3}}{34} = \frac{307}{34}

Divide the numbers

x^{3} = \frac{307}{34}

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

3 x^{3} = 3 \frac{307}{34}

Calculate

x = 3 \frac{307}{34}

Solution

More Steps

Evaluate

3 \frac{307}{34}

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

\frac{3 307}{3 34}

Multiply by the Conjugate

\frac{3 307 \times 3 3 4 ^{2}}{3 34 \times 3 3 4 ^{2}}

Simplify

\frac{3 307 \times 3 1156}{3 34 \times 3 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

3307 \times 31156

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

3 307 \times 1156

Calculate the product

3354892

\frac{3 354892}{3 34 \times 3 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

334 \times 3 3 4^{2}

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

3 34 \times 3 4^{2}

Calculate the product

3 3 4^{3}

Reduce the index of the radical and exponent with 3

34

\frac{3 354892}{34}

x = \frac{3 354892}{34}

Alternative Form

x \approx 2.082347

Show Solution