Solve 8x^2 180x=2436

Question

Solve the equation

x = \frac{3 45675}{30}

Alternative Form

x \approx 1.19153

Evaluate

8 x^{2} \times 180 x = 2436

Multiply

More Steps

Evaluate

8 x^{2} \times 180 x

Multiply the terms

1440 x^{2} \times x

Multiply the terms with the same base by adding their exponents

1440 x^{2 + 1}

Add the numbers

1440 x^{3}

1440 x^{3} = 2436

Divide both sides

\frac{1440 x ^{3}}{1440} = \frac{2436}{1440}

Divide the numbers

x^{3} = \frac{2436}{1440}

Cancel out the common factor 12

x^{3} = \frac{203}{120}

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

3 x^{3} = 3 \frac{203}{120}

Calculate

x = 3 \frac{203}{120}

Solution

More Steps

Evaluate

3 \frac{203}{120}

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

\frac{3 203}{3 120}

Simplify the radical expression

More Steps

Evaluate

3120

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

3 8 \times 15

Write the number in exponential form with the base of 2

3 2^{3} \times 15

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

3 2^{3} \times 315

Reduce the index of the radical and exponent with 3

2315

\frac{3 203}{2 3 15}

Multiply by the Conjugate

\frac{3 203 \times 3 1 5 ^{2}}{2 3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 203 \times 3 225}{2 3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

3203 \times 3225

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

3 203 \times 225

Calculate the product

345675

\frac{3 45675}{2 3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

2315 \times 3 1 5^{2}

Multiply the terms

2 \times 15

Multiply the terms

30

\frac{3 45675}{30}

x = \frac{3 45675}{30}

Alternative Form

x \approx 1.19153

Show Solution