Solve 32x^218x-17=0

Question

Solve the equation

x = \frac{3 51}{12}

Alternative Form

x \approx 0.309036

Evaluate

32 x^{2} \times 18 x - 17 = 0

Multiply

More Steps

Evaluate

32 x^{2} \times 18 x

Multiply the terms

576 x^{2} \times x

Multiply the terms with the same base by adding their exponents

576 x^{2 + 1}

Add the numbers

576 x^{3}

576 x^{3} - 17 = 0

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

576 x^{3} = 0 + 17

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

576 x^{3} = 17

Divide both sides

\frac{576 x ^{3}}{576} = \frac{17}{576}

Divide the numbers

x^{3} = \frac{17}{576}

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

3 x^{3} = 3 \frac{17}{576}

Calculate

x = 3 \frac{17}{576}

Solution

More Steps

Evaluate

3 \frac{17}{576}

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

\frac{3 17}{3 576}

Simplify the radical expression

More Steps

Evaluate

3576

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

3 64 \times 9

Write the number in exponential form with the base of 4

3 4^{3} \times 9

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

3 4^{3} \times 39

Reduce the index of the radical and exponent with 3

439

\frac{3 17}{4 3 9}

Multiply by the Conjugate

\frac{3 17 \times 3 9 ^{2}}{4 3 9 \times 3 9 ^{2}}

Simplify

\frac{3 17 \times 3 3 3}{4 3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

317 \times 333

Multiply the terms

351 \times 3

Use the commutative property to reorder the terms

3351

\frac{3 3 51}{4 3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

439 \times 3 9^{2}

Multiply the terms

4 \times 3^{2}

Multiply the terms

36

\frac{3 3 51}{36}

Cancel out the common factor 3

\frac{3 51}{12}

x = \frac{3 51}{12}

Alternative Form

x \approx 0.309036

Show Solution