Solve x^2 21x-1080=0

Question

x^{2} \times 21 x - 1080 = 0

Solve the equation

x = \frac{2 3 2205}{7}

Alternative Form

x \approx 3.718789

Evaluate

x^{2} \times 21 x - 1080 = 0

Multiply

More Steps

Evaluate

x^{2} \times 21 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 21

Add the numbers

x^{3} \times 21

Use the commutative property to reorder the terms

21 x^{3}

21 x^{3} - 1080 = 0

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

21 x^{3} = 0 + 1080

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

21 x^{3} = 1080

Divide both sides

\frac{21 x ^{3}}{21} = \frac{1080}{21}

Divide the numbers

x^{3} = \frac{1080}{21}

Cancel out the common factor 3

x^{3} = \frac{360}{7}

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

3 x^{3} = 3 \frac{360}{7}

Calculate

x = 3 \frac{360}{7}

Solution

More Steps

Evaluate

3 \frac{360}{7}

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

\frac{3 360}{3 7}

Simplify the radical expression

More Steps

Evaluate

3360

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

3 8 \times 45

Write the number in exponential form with the base of 2

3 2^{3} \times 45

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

3 2^{3} \times 345

Reduce the index of the radical and exponent with 3

2345

\frac{2 3 45}{3 7}

Multiply by the Conjugate

\frac{2 3 45 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{2 3 45 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 349

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

3 45 \times 49

Calculate the product

32205

\frac{2 3 2205}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{2 3 2205}{7}

x = \frac{2 3 2205}{7}

Alternative Form

x \approx 3.718789

Show Solution