Solve 8x^2 13x - 6

Question

Simplify the expression

104 x^{3} - 6

Evaluate

8 x^{2} \times 13 x - 6

Solution

More Steps

Evaluate

8 x^{2} \times 13 x

Multiply the terms

104 x^{2} \times x

Multiply the terms with the same base by adding their exponents

104 x^{2 + 1}

Add the numbers

104 x^{3}

104 x^{3} - 6

Show Solution

Factor the expression

2 (52 x^{3} - 3)

Evaluate

8 x^{2} \times 13 x - 6

Multiply

More Steps

Evaluate

8 x^{2} \times 13 x

Multiply the terms

104 x^{2} \times x

Multiply the terms with the same base by adding their exponents

104 x^{2 + 1}

Add the numbers

104 x^{3}

104 x^{3} - 6

Solution

2 (52 x^{3} - 3)

Show Solution

Find the roots

x = \frac{3 1014}{26}

Alternative Form

x \approx 0.386402

Evaluate

8 x^{2} \times 13 x - 6

To find the roots of the expression,set the expression equal to 0

8 x^{2} \times 13 x - 6 = 0

Multiply

More Steps

Multiply the terms

8 x^{2} \times 13 x

Multiply the terms

104 x^{2} \times x

Multiply the terms with the same base by adding their exponents

104 x^{2 + 1}

Add the numbers

104 x^{3}

104 x^{3} - 6 = 0

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

104 x^{3} = 0 + 6

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

104 x^{3} = 6

Divide both sides

\frac{104 x ^{3}}{104} = \frac{6}{104}

Divide the numbers

x^{3} = \frac{6}{104}

Cancel out the common factor 2

x^{3} = \frac{3}{52}

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

3 x^{3} = 3 \frac{3}{52}

Calculate

x = 3 \frac{3}{52}

Solution

More Steps

Evaluate

3 \frac{3}{52}

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

\frac{3 3}{3 52}

Multiply by the Conjugate

\frac{3 3 \times 3 5 2 ^{2}}{3 52 \times 3 5 2 ^{2}}

Simplify

\frac{3 3 \times 2 3 338}{3 52 \times 3 5 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 23338

Multiply the terms

31014 \times 2

Use the commutative property to reorder the terms

231014

\frac{2 3 1014}{3 52 \times 3 5 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

352 \times 3 5 2^{2}

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

3 52 \times 5 2^{2}

Calculate the product

3 5 2^{3}

Reduce the index of the radical and exponent with 3

52

\frac{2 3 1014}{52}

Cancel out the common factor 2

\frac{3 1014}{26}

x = \frac{3 1014}{26}

Alternative Form

x \approx 0.386402

Show Solution