Solve -x^22x-2=5 - ScanMath

Question

Solve the equation

x = - \frac{3 28}{2}

Alternative Form

x \approx - 1.518294

Evaluate

- x^{2} \times 2 x - 2 = 5

Multiply

More Steps

Evaluate

- x^{2} \times 2 x

Multiply the terms with the same base by adding their exponents

- x^{2 + 1} \times 2

Add the numbers

- x^{3} \times 2

Use the commutative property to reorder the terms

- 2 x^{3}

- 2 x^{3} - 2 = 5

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

- 2 x^{3} = 5 + 2

Add the numbers

- 2 x^{3} = 7

Change the signs on both sides of the equation

2 x^{3} = - 7

Divide both sides

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

Divide the numbers

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

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

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

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

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

Calculate

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

Solution

More Steps

Evaluate

3 - \frac{7}{2}

An odd root of a negative radicand is always a negative

- 3 \frac{7}{2}

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

- \frac{3 7}{3 2}

Multiply by the Conjugate

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

Simplify

\frac{- 3 7 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

- 37 \times 34

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

- 3 7 \times 4

Calculate the product

- 328

\frac{- 3 28}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{- 3 28}{2}

Calculate

- \frac{3 28}{2}

x = - \frac{3 28}{2}

Alternative Form

x \approx - 1.518294

Show Solution