Solve 5x^4=3x-2x^4

Question

Solve the equation

x_{1} = 0, x_{2} = \frac{3 147}{7}

Alternative Form

x_{1} = 0, x_{2} \approx 0.753947

Evaluate

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

Move the expression to the left side

5 x^{4} - (3 x - 2 x^{4}) = 0

Subtract the terms

More Steps

Evaluate

5 x^{4} - (3 x - 2 x^{4})

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

5 x^{4} - 3 x + 2 x^{4}

Add the terms

More Steps

Evaluate

5 x^{4} + 2 x^{4}

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

(5 + 2) x^{4}

Add the numbers

7 x^{4}

7 x^{4} - 3 x

7 x^{4} - 3 x = 0

Factor the expression

x (7 x^{3} - 3) = 0

Separate the equation into 2 possible cases

x = 0 7 x^{3} - 3 = 0

Solve the equation

More Steps

Evaluate

7 x^{3} - 3 = 0

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

7 x^{3} = 0 + 3

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

7 x^{3} = 3

Divide both sides

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

Divide the numbers

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

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

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

Calculate

x = 3 \frac{3}{7}

Simplify the root

More Steps

Evaluate

3 \frac{3}{7}

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

\frac{3 3}{3 7}

Multiply by the Conjugate

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

Simplify

\frac{3 3 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

\frac{3 147}{3 7 \times 3 7 ^{2}}

Multiply the numbers

\frac{3 147}{7}

x = \frac{3 147}{7}

x = 0 x = \frac{3 147}{7}

Solution

x_{1} = 0, x_{2} = \frac{3 147}{7}

Alternative Form

x_{1} = 0, x_{2} \approx 0.753947

Show Solution

Solve the equation

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