Solve -3x^2 45x -78

Question

Simplify the expression

- 135 x^{3} - 78

Evaluate

- 3 x^{2} \times 45 x - 78

Solution

More Steps

Evaluate

- 3 x^{2} \times 45 x

Multiply the terms

- 135 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 135 x^{2 + 1}

Add the numbers

- 135 x^{3}

- 135 x^{3} - 78

Show Solution

Factor the expression

- 3 (45 x^{3} + 26)

Evaluate

- 3 x^{2} \times 45 x - 78

Multiply

More Steps

Evaluate

- 3 x^{2} \times 45 x

Multiply the terms

- 135 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 135 x^{2 + 1}

Add the numbers

- 135 x^{3}

- 135 x^{3} - 78

Solution

- 3 (45 x^{3} + 26)

Show Solution

Find the roots

x = - \frac{3 1950}{15}

Alternative Form

x \approx - 0.832889

Evaluate

- 3 x^{2} \times 45 x - 78

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

- 3 x^{2} \times 45 x - 78 = 0

Multiply

More Steps

Multiply the terms

- 3 x^{2} \times 45 x

Multiply the terms

- 135 x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 135 x^{2 + 1}

Add the numbers

- 135 x^{3}

- 135 x^{3} - 78 = 0

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

- 135 x^{3} = 0 + 78

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

- 135 x^{3} = 78

Change the signs on both sides of the equation

135 x^{3} = - 78

Divide both sides

\frac{135 x ^{3}}{135} = \frac{- 78}{135}

Divide the numbers

x^{3} = \frac{- 78}{135}

Divide the numbers

More Steps

Evaluate

\frac{- 78}{135}

Cancel out the common factor 3

\frac{- 26}{45}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{26}{45}

x^{3} = - \frac{26}{45}

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

3 x^{3} = 3 - \frac{26}{45}

Calculate

x = 3 - \frac{26}{45}

Solution

More Steps

Evaluate

3 - \frac{26}{45}

An odd root of a negative radicand is always a negative

- 3 \frac{26}{45}

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

- \frac{3 26}{3 45}

Multiply by the Conjugate

\frac{- 3 26 \times 3 4 5 ^{2}}{3 45 \times 3 4 5 ^{2}}

Simplify

\frac{- 3 26 \times 3 3 75}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 326 \times 3375

Multiply the terms

- 31950 \times 3

Use the commutative property to reorder the terms

- 331950

\frac{- 3 3 1950}{3 45 \times 3 4 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

345 \times 3 4 5^{2}

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

3 45 \times 4 5^{2}

Calculate the product

3 4 5^{3}

Reduce the index of the radical and exponent with 3

45

\frac{- 3 3 1950}{45}

Cancel out the common factor 3

\frac{- 3 1950}{15}

Calculate

- \frac{3 1950}{15}

x = - \frac{3 1950}{15}

Alternative Form

x \approx - 0.832889

Show Solution