Solve 2x^4-5x^23=0

Question

Solve the equation

x_{1} = - \frac{30}{2}, x_{2} = 0, x_{3} = \frac{30}{2}

Alternative Form

x_{1} \approx - 2.738613, x_{2} = 0, x_{3} \approx 2.738613

Evaluate

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

Multiply the terms

2 x^{4} - 15 x^{2} = 0

Factor the expression

x^{2} (2 x^{2} - 15) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 x^{2} - 15 = 0

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

x = 0 2 x^{2} - 15 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 15 = 0

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

2 x^{2} = 0 + 15

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

2 x^{2} = 15

Divide both sides

\frac{2 x ^{2}}{2} = \frac{15}{2}

Divide the numbers

x^{2} = \frac{15}{2}

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

x = \pm \frac{15}{2}

Simplify the expression

More Steps

Evaluate

\frac{15}{2}

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

\frac{15}{2}

Multiply by the Conjugate

\frac{15 \times 2}{2 \times 2}

Multiply the numbers

\frac{30}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{30}{2}

x = \pm \frac{30}{2}

Separate the equation into 2 possible cases

x = \frac{30}{2} x = - \frac{30}{2}

x = 0 x = \frac{30}{2} x = - \frac{30}{2}

Solution

x_{1} = - \frac{30}{2}, x_{2} = 0, x_{3} = \frac{30}{2}

Alternative Form

x_{1} \approx - 2.738613, x_{2} = 0, x_{3} \approx 2.738613

Show Solution