Solve 6x^2 3x-38=0

Question

Solve the equation

x = \frac{3 57}{3}

Alternative Form

x \approx 1.282834

Evaluate

6 x^{2} \times 3 x - 38 = 0

Multiply

More Steps

Evaluate

6 x^{2} \times 3 x

Multiply the terms

18 x^{2} \times x

Multiply the terms with the same base by adding their exponents

18 x^{2 + 1}

Add the numbers

18 x^{3}

18 x^{3} - 38 = 0

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

18 x^{3} = 0 + 38

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

18 x^{3} = 38

Divide both sides

\frac{18 x ^{3}}{18} = \frac{38}{18}

Divide the numbers

x^{3} = \frac{38}{18}

Cancel out the common factor 2

x^{3} = \frac{19}{9}

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

3 x^{3} = 3 \frac{19}{9}

Calculate

x = 3 \frac{19}{9}

Solution

More Steps

Evaluate

3 \frac{19}{9}

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

\frac{3 19}{3 9}

Multiply by the Conjugate

\frac{3 19 \times 3 9 ^{2}}{3 9 \times 3 9 ^{2}}

Simplify

\frac{3 19 \times 3 3 3}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

319 \times 333

Multiply the terms

357 \times 3

Use the commutative property to reorder the terms

3357

\frac{3 3 57}{3 9 \times 3 9 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 3 9^{2}

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

3 9 \times 9^{2}

Calculate the product

3 9^{3}

Transform the expression

3 3^{6}

Reduce the index of the radical and exponent with 3

3^{2}

\frac{3 3 57}{3 ^{2}}

Reduce the fraction

More Steps

Evaluate

\frac{3}{3 ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{3 ^{2 - 1}}

Subtract the terms

\frac{1}{3 ^{1}}

Simplify

\frac{1}{3}

\frac{3 57}{3}

x = \frac{3 57}{3}

Alternative Form

x \approx 1.282834

Show Solution