Solve 4x^4-25x^2 6

Question

Simplify the expression

4 x^{4} - 150 x^{2}

Evaluate

4 x^{4} - 25 x^{2} \times 6

Solution

4 x^{4} - 150 x^{2}

Show Solution

2 x^{2} (2 x^{2} - 75)

Evaluate

4 x^{4} - 25 x^{2} \times 6

Multiply the terms

4 x^{4} - 150 x^{2}

Rewrite the expression

2 x^{2} \times 2 x^{2} - 2 x^{2} \times 75

Solution

2 x^{2} (2 x^{2} - 75)

Show Solution

x_{1} = - \frac{5 6}{2}, x_{2} = 0, x_{3} = \frac{5 6}{2}

Alternative Form

x_{1} \approx - 6.123724, x_{2} = 0, x_{3} \approx 6.123724

Evaluate

4 x^{4} - 25 x^{2} \times 6

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

4 x^{4} - 25 x^{2} \times 6 = 0

Multiply the terms

4 x^{4} - 150 x^{2} = 0

Factor the expression

2 x^{2} (2 x^{2} - 75) = 0

Divide both sides

x^{2} (2 x^{2} - 75) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 x^{2} - 75 = 0

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

x = 0 2 x^{2} - 75 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 75 = 0

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

2 x^{2} = 0 + 75

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

2 x^{2} = 75

Divide both sides

\frac{2 x ^{2}}{2} = \frac{75}{2}

Divide the numbers

x^{2} = \frac{75}{2}

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

x = \pm \frac{75}{2}

Simplify the expression

More Steps

Evaluate

\frac{75}{2}

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

\frac{75}{2}

Simplify the radical expression

\frac{5 3}{2}

Multiply by the Conjugate

\frac{5 3 \times 2}{2 \times 2}

Multiply the numbers

\frac{5 6}{2 \times 2}

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

\frac{5 6}{2}

x = \pm \frac{5 6}{2}

Separate the equation into 2 possible cases

x = \frac{5 6}{2} x = - \frac{5 6}{2}

x = 0 x = \frac{5 6}{2} x = - \frac{5 6}{2}

Solution

x_{1} = - \frac{5 6}{2}, x_{2} = 0, x_{3} = \frac{5 6}{2}

Alternative Form

x_{1} \approx - 6.123724, x_{2} = 0, x_{3} \approx 6.123724

Show Solution