Solve 8x^2 30x - 27 = 0

Question

Solve the equation

x = \frac{3 900}{20}

Alternative Form

x \approx 0.482745

Evaluate

8 x^{2} \times 30 x - 27 = 0

Multiply

More Steps

Evaluate

8 x^{2} \times 30 x

Multiply the terms

240 x^{2} \times x

Multiply the terms with the same base by adding their exponents

240 x^{2 + 1}

Add the numbers

240 x^{3}

240 x^{3} - 27 = 0

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

240 x^{3} = 0 + 27

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

240 x^{3} = 27

Divide both sides

\frac{240 x ^{3}}{240} = \frac{27}{240}

Divide the numbers

x^{3} = \frac{27}{240}

Cancel out the common factor 3

x^{3} = \frac{9}{80}

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

3 x^{3} = 3 \frac{9}{80}

Calculate

x = 3 \frac{9}{80}

Solution

More Steps

Evaluate

3 \frac{9}{80}

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

\frac{3 9}{3 80}

Simplify the radical expression

More Steps

Evaluate

380

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 10

Write the number in exponential form with the base of 2

3 2^{3} \times 10

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 310

Reduce the index of the radical and exponent with 3

2310

\frac{3 9}{2 3 10}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

2310 \times 3 1 0^{2}

Multiply the terms

2 \times 10

Multiply the terms

20

\frac{3 900}{20}

x = \frac{3 900}{20}

Alternative Form

x \approx 0.482745

Show Solution