Solve x^2 7x-270 - ScanMath

Question

Simplify the expression

7 x^{3} - 270

Evaluate

x^{2} \times 7 x - 270

Solution

More Steps

Evaluate

x^{2} \times 7 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 7

Add the numbers

x^{3} \times 7

Use the commutative property to reorder the terms

7 x^{3}

7 x^{3} - 270

Show Solution

x = \frac{3 3 490}{7}

Alternative Form

x \approx 3.378744

Evaluate

x^{2} \times 7 x - 270

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

x^{2} \times 7 x - 270 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 7 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 7

Add the numbers

x^{3} \times 7

Use the commutative property to reorder the terms

7 x^{3}

7 x^{3} - 270 = 0

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

7 x^{3} = 0 + 270

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

7 x^{3} = 270

Divide both sides

\frac{7 x ^{3}}{7} = \frac{270}{7}

Divide the numbers

x^{3} = \frac{270}{7}

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

3 x^{3} = 3 \frac{270}{7}

Calculate

x = 3 \frac{270}{7}

Solution

More Steps

Evaluate

3 \frac{270}{7}

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

\frac{3 270}{3 7}

Simplify the radical expression

More Steps

Evaluate

3270

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

3 27 \times 10

Write the number in exponential form with the base of 3

3 3^{3} \times 10

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

3 3^{3} \times 310

Reduce the index of the radical and exponent with 3

3310

\frac{3 3 10}{3 7}

Multiply by the Conjugate

\frac{3 3 10 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 3 10 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 349

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

3 10 \times 49

Calculate the product

3490

\frac{3 3 490}{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{3 3 490}{7}

x = \frac{3 3 490}{7}

Alternative Form

x \approx 3.378744

Show Solution