Solve (2x^(2) 7x-15)^(3)

Question

Simplify the expression

2744 x^{9} - 8820 x^{6} + 9450 x^{3} - 3375

Evaluate

(2 x^{2} \times 7 x - 15)^{3}

Multiply

More Steps

Evaluate

2 x^{2} \times 7 x

Multiply the terms

14 x^{2} \times x

Multiply the terms with the same base by adding their exponents

14 x^{2 + 1}

Add the numbers

14 x^{3}

(14 x^{3} - 15)^{3}

Use (a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} to expand the expression

(14 x^{3})^{3} - 3 (14 x^{3})^{2} \times 15 + 3 \times 14 x^{3} \times 1 5^{2} - 1 5^{3}

Solution

2744 x^{9} - 8820 x^{6} + 9450 x^{3} - 3375

Show Solution

x = \frac{3 2940}{14}

Alternative Form

x \approx 1.023264

Evaluate

(2 x^{2} \times 7 x - 15)^{3}

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

(2 x^{2} \times 7 x - 15)^{3} = 0

Multiply

More Steps

Multiply the terms

2 x^{2} \times 7 x

Multiply the terms

14 x^{2} \times x

Multiply the terms with the same base by adding their exponents

14 x^{2 + 1}

Add the numbers

14 x^{3}

(14 x^{3} - 15)^{3} = 0

The only way a power can be 0 is when the base equals 0

14 x^{3} - 15 = 0

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

14 x^{3} = 0 + 15

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

14 x^{3} = 15

Divide both sides

\frac{14 x ^{3}}{14} = \frac{15}{14}

Divide the numbers

x^{3} = \frac{15}{14}

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

3 x^{3} = 3 \frac{15}{14}

Calculate

x = 3 \frac{15}{14}

Solution

More Steps

Evaluate

3 \frac{15}{14}

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

\frac{3 15}{3 14}

Multiply by the Conjugate

\frac{3 15 \times 3 1 4 ^{2}}{3 14 \times 3 1 4 ^{2}}

Simplify

\frac{3 15 \times 3 196}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

315 \times 3196

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

3 15 \times 196

Calculate the product

32940

\frac{3 2940}{3 14 \times 3 1 4 ^{2}}

Multiply the numbers

More Steps

Evaluate

314 \times 3 1 4^{2}

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

3 14 \times 1 4^{2}

Calculate the product

3 1 4^{3}

Reduce the index of the radical and exponent with 3

14

\frac{3 2940}{14}

x = \frac{3 2940}{14}

Alternative Form

x \approx 1.023264

Show Solution