Solve -x^2 7x-6 - ScanMath

Question

Simplify the expression

- 7 x^{3} - 6

Evaluate

- x^{2} \times 7 x - 6

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} - 6

Show Solution

x = - \frac{3 294}{7}

Alternative Form

x \approx - 0.949914

Evaluate

- x^{2} \times 7 x - 6

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

- x^{2} \times 7 x - 6 = 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} - 6 = 0

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

- 7 x^{3} = 0 + 6

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

- 7 x^{3} = 6

Change the signs on both sides of the equation

7 x^{3} = - 6

Divide both sides

\frac{7 x ^{3}}{7} = \frac{- 6}{7}

Divide the numbers

x^{3} = \frac{- 6}{7}

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

x^{3} = - \frac{6}{7}

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

3 x^{3} = 3 - \frac{6}{7}

Calculate

x = 3 - \frac{6}{7}

Solution

More Steps

Evaluate

3 - \frac{6}{7}

An odd root of a negative radicand is always a negative

- 3 \frac{6}{7}

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

- \frac{3 6}{3 7}

Multiply by the Conjugate

\frac{- 3 6 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{- 3 6 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 36 \times 349

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

- 3 6 \times 49

Calculate the product

- 3294

\frac{- 3 294}{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{- 3 294}{7}

Calculate

- \frac{3 294}{7}

x = - \frac{3 294}{7}

Alternative Form

x \approx - 0.949914

Show Solution