Solve -8x^5=-6x^3

Question

Solve the equation

x_{1} = - \frac{3}{2}, x_{2} = 0, x_{3} = \frac{3}{2}

Alternative Form

x_{1} \approx - 0.866025, x_{2} = 0, x_{3} \approx 0.866025

Evaluate

- 8 x^{5} = - 6 x^{3}

Add or subtract both sides

- 8 x^{5} - (- 6 x^{3}) = 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

- 8 x^{5} + 6 x^{3} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

x^{3} = 0 - 4 x^{2} + 3 = 0

The only way a power can be 0 is when the base equals 0

x = 0 - 4 x^{2} + 3 = 0

Solve the equation

More Steps

Evaluate

- 4 x^{2} + 3 = 0

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

- 4 x^{2} = 0 - 3

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

- 4 x^{2} = - 3

Change the signs on both sides of the equation

4 x^{2} = 3

Divide both sides

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{3}{4}

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

\frac{3}{4}

Simplify the radical expression

\frac{3}{2}

x = \pm \frac{3}{2}

Separate the equation into 2 possible cases

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

x = 0 x = \frac{3}{2} x = - \frac{3}{2}

Solution

x_{1} = - \frac{3}{2}, x_{2} = 0, x_{3} = \frac{3}{2}

Alternative Form

x_{1} \approx - 0.866025, x_{2} = 0, x_{3} \approx 0.866025

Show Solution

Solve the equation

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