Solve (x^4)/5 -x^4= x/3 - (x-2)/2

Question

Solve the equation(The real numbers system)

x \in / R

Evaluate

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

Multiply both sides of the equation by LCD

(\frac{x ^{4}}{5} - x^{4}) \times 30 = (\frac{x}{3} - \frac{x - 2}{2}) \times 30

Simplify the equation

More Steps

Evaluate

(\frac{x ^{4}}{5} - x^{4}) \times 30

Apply the distributive property

\frac{x ^{4}}{5} \times 30 - x^{4} \times 30

Simplify

x^{4} \times 6 - x^{4} \times 30

Use the commutative property to reorder the terms

6 x^{4} - x^{4} \times 30

Use the commutative property to reorder the terms

6 x^{4} - 30 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(6 - 30) x^{4}

Subtract the numbers

- 24 x^{4}

- 24 x^{4} = (\frac{x}{3} - \frac{x - 2}{2}) \times 30

Simplify the equation

More Steps

Evaluate

(\frac{x}{3} - \frac{x - 2}{2}) \times 30

Apply the distributive property

\frac{x}{3} \times 30 - \frac{x - 2}{2} \times 30

Simplify

x \times 10 + (- x + 2) \times 15

Use the commutative property to reorder the terms

10 x + (- x + 2) \times 15

Multiply the terms

More Steps

Evaluate

(- x + 2) \times 15

Apply the distributive property

- x \times 15 + 2 \times 15

Use the commutative property to reorder the terms

- 15 x + 2 \times 15

Calculate

- 15 x + 30

10 x - 15 x + 30

Subtract the terms

More Steps

Evaluate

10 x - 15 x

Collect like terms by calculating the sum or difference of their coefficients

(10 - 15) x

Subtract the numbers

- 5 x

- 5 x + 30

- 24 x^{4} = - 5 x + 30

Move the expression to the left side

- 24 x^{4} - (- 5 x + 30) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 24 x^{4} + 5 x - 30 = 0

Solution

x \in / R

Show Solution

Solve the equation(The complex numbers system)

x_{1} \approx 0.748398 + 0.700361 i, x_{2} \approx 0.748398 - 0.700361 i, x_{3} \approx - 0.748398 + 0.793531 i, x_{4} \approx - 0.748398 - 0.793531 i

Evaluate

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

Multiply both sides of the equation by LCD

(\frac{x ^{4}}{5} - x^{4}) \times 30 = (\frac{x}{3} - \frac{x - 2}{2}) \times 30

Simplify the equation

More Steps

Evaluate

(\frac{x ^{4}}{5} - x^{4}) \times 30

Apply the distributive property

\frac{x ^{4}}{5} \times 30 - x^{4} \times 30

Simplify

x^{4} \times 6 - x^{4} \times 30

Use the commutative property to reorder the terms

6 x^{4} - x^{4} \times 30

Use the commutative property to reorder the terms

6 x^{4} - 30 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(6 - 30) x^{4}

Subtract the numbers

- 24 x^{4}

- 24 x^{4} = (\frac{x}{3} - \frac{x - 2}{2}) \times 30

Simplify the equation

More Steps

Evaluate

(\frac{x}{3} - \frac{x - 2}{2}) \times 30

Apply the distributive property

\frac{x}{3} \times 30 - \frac{x - 2}{2} \times 30

Simplify

x \times 10 + (- x + 2) \times 15

Use the commutative property to reorder the terms

10 x + (- x + 2) \times 15

Multiply the terms

More Steps

Evaluate

(- x + 2) \times 15

Apply the distributive property

- x \times 15 + 2 \times 15

Use the commutative property to reorder the terms

- 15 x + 2 \times 15

Calculate

- 15 x + 30

10 x - 15 x + 30

Subtract the terms

More Steps

Evaluate

10 x - 15 x

Collect like terms by calculating the sum or difference of their coefficients

(10 - 15) x

Subtract the numbers

- 5 x

- 5 x + 30

- 24 x^{4} = - 5 x + 30

Move the expression to the left side

- 24 x^{4} - (- 5 x + 30) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 24 x^{4} + 5 x - 30 = 0

Calculate

x \approx - 0.748398 - 0.793531 i x \approx - 0.748398 + 0.793531 i x \approx 0.748398 - 0.700361 i x \approx 0.748398 + 0.700361 i

Solution

x_{1} \approx 0.748398 + 0.700361 i, x_{2} \approx 0.748398 - 0.700361 i, x_{3} \approx - 0.748398 + 0.793531 i, x_{4} \approx - 0.748398 - 0.793531 i

Show Solution

Solve the equation(The real numbers system)

Solve the equation(The complex numbers system)

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