Solve 4x^4 - 37x^29

Question

Simplify the expression

4 x^{4} - 333 x^{2}

Evaluate

4 x^{4} - 37 x^{2} \times 9

Solution

4 x^{4} - 333 x^{2}

Show Solution

x^{2} (4 x^{2} - 333)

Evaluate

4 x^{4} - 37 x^{2} \times 9

Multiply the terms

4 x^{4} - 333 x^{2}

Rewrite the expression

x^{2} \times 4 x^{2} - x^{2} \times 333

Solution

x^{2} (4 x^{2} - 333)

Show Solution

x_{1} = - \frac{3 37}{2}, x_{2} = 0, x_{3} = \frac{3 37}{2}

Alternative Form

x_{1} \approx - 9.124144, x_{2} = 0, x_{3} \approx 9.124144

Evaluate

4 x^{4} - 37 x^{2} \times 9

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

4 x^{4} - 37 x^{2} \times 9 = 0

Multiply the terms

4 x^{4} - 333 x^{2} = 0

Factor the expression

x^{2} (4 x^{2} - 333) = 0

Separate the equation into 2 possible cases

x^{2} = 0 4 x^{2} - 333 = 0

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

x = 0 4 x^{2} - 333 = 0

Solve the equation

More Steps

Evaluate

4 x^{2} - 333 = 0

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

4 x^{2} = 0 + 333

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

4 x^{2} = 333

Divide both sides

\frac{4 x ^{2}}{4} = \frac{333}{4}

Divide the numbers

x^{2} = \frac{333}{4}

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

x = \pm \frac{333}{4}

Simplify the expression

More Steps

Evaluate

\frac{333}{4}

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

\frac{333}{4}

Simplify the radical expression

\frac{3 37}{4}

Simplify the radical expression

\frac{3 37}{2}

x = \pm \frac{3 37}{2}

Separate the equation into 2 possible cases

x = \frac{3 37}{2} x = - \frac{3 37}{2}

x = 0 x = \frac{3 37}{2} x = - \frac{3 37}{2}

Solution

x_{1} = - \frac{3 37}{2}, x_{2} = 0, x_{3} = \frac{3 37}{2}

Alternative Form

x_{1} \approx - 9.124144, x_{2} = 0, x_{3} \approx 9.124144

Show Solution