Solve 3x^28x-13=0

Question

Solve the equation

x = \frac{3 117}{6}

Alternative Form

x \approx 0.815162

Evaluate

3 x^{2} \times 8 x - 13 = 0

Multiply

More Steps

Evaluate

3 x^{2} \times 8 x

Multiply the terms

24 x^{2} \times x

Multiply the terms with the same base by adding their exponents

24 x^{2 + 1}

Add the numbers

24 x^{3}

24 x^{3} - 13 = 0

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

24 x^{3} = 0 + 13

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

24 x^{3} = 13

Divide both sides

\frac{24 x ^{3}}{24} = \frac{13}{24}

Divide the numbers

x^{3} = \frac{13}{24}

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

3 x^{3} = 3 \frac{13}{24}

Calculate

x = 3 \frac{13}{24}

Solution

More Steps

Evaluate

3 \frac{13}{24}

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

\frac{3 13}{3 24}

Simplify the radical expression

More Steps

Evaluate

324

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

3 8 \times 3

Write the number in exponential form with the base of 2

3 2^{3} \times 3

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

3 2^{3} \times 33

Reduce the index of the radical and exponent with 3

233

\frac{3 13}{2 3 3}

Multiply by the Conjugate

\frac{3 13 \times 3 3 ^{2}}{2 3 3 \times 3 3 ^{2}}

Simplify

\frac{3 13 \times 3 9}{2 3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

313 \times 39

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

3 13 \times 9

Calculate the product

3117

\frac{3 117}{2 3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

233 \times 3 3^{2}

Multiply the terms

2 \times 3

Multiply the terms

6

\frac{3 117}{6}

x = \frac{3 117}{6}

Alternative Form

x \approx 0.815162

Show Solution