Solve 12x^2 17x-40

Question

Simplify the expression

204 x^{3} - 40

Evaluate

12 x^{2} \times 17 x - 40

Solution

More Steps

Evaluate

12 x^{2} \times 17 x

Multiply the terms

204 x^{2} \times x

Multiply the terms with the same base by adding their exponents

204 x^{2 + 1}

Add the numbers

204 x^{3}

204 x^{3} - 40

Show Solution

Factor the expression

4 (51 x^{3} - 10)

Evaluate

12 x^{2} \times 17 x - 40

Multiply

More Steps

Evaluate

12 x^{2} \times 17 x

Multiply the terms

204 x^{2} \times x

Multiply the terms with the same base by adding their exponents

204 x^{2 + 1}

Add the numbers

204 x^{3}

204 x^{3} - 40

Solution

4 (51 x^{3} - 10)

Show Solution

Find the roots

x = \frac{3 26010}{51}

Alternative Form

x \approx 0.580956

Evaluate

12 x^{2} \times 17 x - 40

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

12 x^{2} \times 17 x - 40 = 0

Multiply

More Steps

Multiply the terms

12 x^{2} \times 17 x

Multiply the terms

204 x^{2} \times x

Multiply the terms with the same base by adding their exponents

204 x^{2 + 1}

Add the numbers

204 x^{3}

204 x^{3} - 40 = 0

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

204 x^{3} = 0 + 40

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

204 x^{3} = 40

Divide both sides

\frac{204 x ^{3}}{204} = \frac{40}{204}

Divide the numbers

x^{3} = \frac{40}{204}

Cancel out the common factor 4

x^{3} = \frac{10}{51}

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

3 x^{3} = 3 \frac{10}{51}

Calculate

x = 3 \frac{10}{51}

Solution

More Steps

Evaluate

3 \frac{10}{51}

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

\frac{3 10}{3 51}

Multiply by the Conjugate

\frac{3 10 \times 3 5 1 ^{2}}{3 51 \times 3 5 1 ^{2}}

Simplify

\frac{3 10 \times 3 2601}{3 51 \times 3 5 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

310 \times 32601

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

3 10 \times 2601

Calculate the product

326010

\frac{3 26010}{3 51 \times 3 5 1 ^{2}}

Multiply the numbers

More Steps

Evaluate

351 \times 3 5 1^{2}

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

3 51 \times 5 1^{2}

Calculate the product

3 5 1^{3}

Reduce the index of the radical and exponent with 3

51

\frac{3 26010}{51}

x = \frac{3 26010}{51}

Alternative Form

x \approx 0.580956

Show Solution