Solve x^236x-1323=0

Question

x^{2} \times 36 x - 1323 = 0

Solve the equation

x = \frac{3 294}{2}

Alternative Form

x \approx 3.3247

Evaluate

x^{2} \times 36 x - 1323 = 0

Multiply

More Steps

Evaluate

x^{2} \times 36 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 36

Add the numbers

x^{3} \times 36

Use the commutative property to reorder the terms

36 x^{3}

36 x^{3} - 1323 = 0

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

36 x^{3} = 0 + 1323

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

36 x^{3} = 1323

Divide both sides

\frac{36 x ^{3}}{36} = \frac{1323}{36}

Divide the numbers

x^{3} = \frac{1323}{36}

Cancel out the common factor 9

x^{3} = \frac{147}{4}

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

3 x^{3} = 3 \frac{147}{4}

Calculate

x = 3 \frac{147}{4}

Solution

More Steps

Evaluate

3 \frac{147}{4}

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

\frac{3 147}{3 4}

Multiply by the Conjugate

\frac{3 147 \times 3 4 ^{2}}{3 4 \times 3 4 ^{2}}

Simplify

\frac{3 147 \times 2 3 2}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

3147 \times 232

Multiply the terms

3294 \times 2

Use the commutative property to reorder the terms

23294

\frac{2 3 294}{3 4 \times 3 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

34 \times 3 4^{2}

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

3 4 \times 4^{2}

Calculate the product

3 4^{3}

Transform the expression

3 2^{6}

Reduce the index of the radical and exponent with 3

2^{2}

\frac{2 3 294}{2 ^{2}}

Reduce the fraction

More Steps

Evaluate

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

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

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

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{3 294}{2}

x = \frac{3 294}{2}

Alternative Form

x \approx 3.3247

Show Solution