Solve 2x-45x^5 - ScanMath

Question

Factor the expression

x (2 - 45 x^{4})

Evaluate

2 x - 45 x^{5}

Rewrite the expression

x \times 2 - x \times 45 x^{4}

Solution

x (2 - 45 x^{4})

Show Solution

x_{1} = - \frac{4 2 \times 4 5 ^{3}}{45}, x_{2} = 0, x_{3} = \frac{4 2 \times 4 5 ^{3}}{45}

Alternative Form

x_{1} \approx - 0.45915, x_{2} = 0, x_{3} \approx 0.45915

Evaluate

2 x - 45 x^{5}

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

2 x - 45 x^{5} = 0

Factor the expression

x (2 - 45 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 2 - 45 x^{4} = 0

Solve the equation

More Steps

Evaluate

2 - 45 x^{4} = 0

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

- 45 x^{4} = 0 - 2

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

- 45 x^{4} = - 2

Change the signs on both sides of the equation

45 x^{4} = 2

Divide both sides

\frac{45 x ^{4}}{45} = \frac{2}{45}

Divide the numbers

x^{4} = \frac{2}{45}

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

x = \pm 4 \frac{2}{45}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{45}

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

\frac{4 2}{4 45}

Multiply by the Conjugate

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

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

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

Multiply the numbers

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

x = \pm \frac{4 2 \times 4 5 ^{3}}{45}

Separate the equation into 2 possible cases

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

x = 0 x = \frac{4 2 \times 4 5 ^{3}}{45} x = - \frac{4 2 \times 4 5 ^{3}}{45}

Solution

x_{1} = - \frac{4 2 \times 4 5 ^{3}}{45}, x_{2} = 0, x_{3} = \frac{4 2 \times 4 5 ^{3}}{45}

Alternative Form

x_{1} \approx - 0.45915, x_{2} = 0, x_{3} \approx 0.45915

Show Solution