Solve 9=3-4x^6x - ScanMath

Question

Solve the equation

x = - \frac{7 192}{2}

Alternative Form

x \approx - 1.059634

Evaluate

9 = 3 - 4 x^{6} \times x

Multiply

More Steps

Evaluate

4 x^{6} \times x

Multiply the terms with the same base by adding their exponents

4 x^{6 + 1}

Add the numbers

4 x^{7}

9 = 3 - 4 x^{7}

Swap the sides of the equation

3 - 4 x^{7} = 9

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

- 4 x^{7} = 9 - 3

Subtract the numbers

- 4 x^{7} = 6

Change the signs on both sides of the equation

4 x^{7} = - 6

Divide both sides

\frac{4 x ^{7}}{4} = \frac{- 6}{4}

Divide the numbers

x^{7} = \frac{- 6}{4}

Divide the numbers

More Steps

Evaluate

\frac{- 6}{4}

Cancel out the common factor 2

\frac{- 3}{2}

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

- \frac{3}{2}

x^{7} = - \frac{3}{2}

Take the 7 -th root on both sides of the equation

7 x^{7} = 7 - \frac{3}{2}

Calculate

x = 7 - \frac{3}{2}

Solution

More Steps

Evaluate

7 - \frac{3}{2}

An odd root of a negative radicand is always a negative

- 7 \frac{3}{2}

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

- \frac{7 3}{7 2}

Multiply by the Conjugate

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

Simplify

\frac{- 7 3 \times 7 64}{7 2 \times 7 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

- 73 \times 764

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

- 7 3 \times 64

Calculate the product

- 7192

\frac{- 7 192}{7 2 \times 7 2 ^{6}}

Multiply the numbers

More Steps

Evaluate

72 \times 7 2^{6}

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

7 2 \times 2^{6}

Calculate the product

7 2^{7}

Reduce the index of the radical and exponent with 7

2

\frac{- 7 192}{2}

Calculate

- \frac{7 192}{2}

x = - \frac{7 192}{2}

Alternative Form

x \approx - 1.059634

Show Solution