Solve 5x^2 6x-27 - ScanMath

Question

Simplify the expression

30 x^{3} - 27

Evaluate

5 x^{2} \times 6 x - 27

Solution

More Steps

Evaluate

5 x^{2} \times 6 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 27

Show Solution

Factor the expression

3 (10 x^{3} - 9)

Evaluate

5 x^{2} \times 6 x - 27

Multiply

More Steps

Evaluate

5 x^{2} \times 6 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 27

Solution

3 (10 x^{3} - 9)

Show Solution

Find the roots

x = \frac{3 900}{10}

Alternative Form

x \approx 0.965489

Evaluate

5 x^{2} \times 6 x - 27

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

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

Multiply

More Steps

Multiply the terms

5 x^{2} \times 6 x

Multiply the terms

30 x^{2} \times x

Multiply the terms with the same base by adding their exponents

30 x^{2 + 1}

Add the numbers

30 x^{3}

30 x^{3} - 27 = 0

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

30 x^{3} = 0 + 27

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

30 x^{3} = 27

Divide both sides

\frac{30 x ^{3}}{30} = \frac{27}{30}

Divide the numbers

x^{3} = \frac{27}{30}

Cancel out the common factor 3

x^{3} = \frac{9}{10}

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

3 x^{3} = 3 \frac{9}{10}

Calculate

x = 3 \frac{9}{10}

Solution

More Steps

Evaluate

3 \frac{9}{10}

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

\frac{3 9}{3 10}

Multiply by the Conjugate

\frac{3 9 \times 3 1 0 ^{2}}{3 10 \times 3 1 0 ^{2}}

Simplify

\frac{3 9 \times 3 100}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

39 \times 3100

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

3 9 \times 100

Calculate the product

3900

\frac{3 900}{3 10 \times 3 1 0 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 3 1 0^{2}

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

3 10 \times 1 0^{2}

Calculate the product

3 1 0^{3}

Reduce the index of the radical and exponent with 3

10

\frac{3 900}{10}

x = \frac{3 900}{10}

Alternative Form

x \approx 0.965489

Show Solution