Solve |-5x^3x-2|=5

Question

Solve the equation

x_{1} = - \frac{4 375}{5}, x_{2} = \frac{4 375}{5}

Alternative Form

x_{1} \approx - 0.880112, x_{2} \approx 0.880112

Evaluate

- 5 x^{3} \times x - 2 = 5

Simplify

More Steps

Evaluate

- 5 x^{3} \times x - 2

Multiply

More Steps

Multiply the terms

- 5 x^{3} \times x

Multiply the terms with the same base by adding their exponents

- 5 x^{3 + 1}

Add the numbers

- 5 x^{4}

- 5 x^{4} - 2

Rewrite the expression

5 x^{4} + 2

When the expression in absolute value bars is not negative, remove the bars

5 x^{4} + 2

5 x^{4} + 2 = 5

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

5 x^{4} = 5 - 2

Subtract the numbers

5 x^{4} = 3

Divide both sides

\frac{5 x ^{4}}{5} = \frac{3}{5}

Divide the numbers

x^{4} = \frac{3}{5}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{3}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{5}

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

\frac{4 3}{4 5}

Multiply by the Conjugate

\frac{4 3 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 3 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4125

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

4 3 \times 125

Calculate the product

4375

\frac{4 375}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{4 375}{5}

x = \pm \frac{4 375}{5}

Separate the equation into 2 possible cases

x = \frac{4 375}{5} x = - \frac{4 375}{5}

Solution

x_{1} = - \frac{4 375}{5}, x_{2} = \frac{4 375}{5}

Alternative Form

x_{1} \approx - 0.880112, x_{2} \approx 0.880112

Show Solution