Solve x^2 6x-27 - ScanMath

Question

Simplify the expression

6 x^{3} - 27

Evaluate

x^{2} \times 6 x - 27

Solution

More Steps

Evaluate

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

6 x^{3} - 27

Show Solution

Factor the expression

3 (2 x^{3} - 9)

Evaluate

x^{2} \times 6 x - 27

Multiply

More Steps

Evaluate

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

6 x^{3} - 27

Solution

3 (2 x^{3} - 9)

Show Solution

Find the roots

x = \frac{3 36}{2}

Alternative Form

x \approx 1.650964

Evaluate

x^{2} \times 6 x - 27

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

x^{2} \times 6 x - 27 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 6

Add the numbers

x^{3} \times 6

Use the commutative property to reorder the terms

6 x^{3}

6 x^{3} - 27 = 0

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

6 x^{3} = 0 + 27

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

6 x^{3} = 27

Divide both sides

\frac{6 x ^{3}}{6} = \frac{27}{6}

Divide the numbers

x^{3} = \frac{27}{6}

Cancel out the common factor 3

x^{3} = \frac{9}{2}

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

3 x^{3} = 3 \frac{9}{2}

Calculate

x = 3 \frac{9}{2}

Solution

More Steps

Evaluate

3 \frac{9}{2}

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

\frac{3 9}{3 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

39 \times 34

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

3 9 \times 4

Calculate the product

336

\frac{3 36}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 36}{2}

x = \frac{3 36}{2}

Alternative Form

x \approx 1.650964

Show Solution