Solve 16x^4-40x^25

Question

Simplify the expression

16 x^{4} - 200 x^{2}

Evaluate

16 x^{4} - 40 x^{2} \times 5

Solution

16 x^{4} - 200 x^{2}

Show Solution

8 x^{2} (2 x^{2} - 25)

Evaluate

16 x^{4} - 40 x^{2} \times 5

Multiply the terms

16 x^{4} - 200 x^{2}

Rewrite the expression

8 x^{2} \times 2 x^{2} - 8 x^{2} \times 25

Solution

8 x^{2} (2 x^{2} - 25)

Show Solution

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

Alternative Form

x_{1} \approx - 3.535534, x_{2} = 0, x_{3} \approx 3.535534

Evaluate

16 x^{4} - 40 x^{2} \times 5

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

16 x^{4} - 40 x^{2} \times 5 = 0

Multiply the terms

16 x^{4} - 200 x^{2} = 0

Factor the expression

8 x^{2} (2 x^{2} - 25) = 0

Divide both sides

x^{2} (2 x^{2} - 25) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 x^{2} - 25 = 0

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

x = 0 2 x^{2} - 25 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 25 = 0

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

2 x^{2} = 0 + 25

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

2 x^{2} = 25

Divide both sides

\frac{2 x ^{2}}{2} = \frac{25}{2}

Divide the numbers

x^{2} = \frac{25}{2}

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

x = \pm \frac{25}{2}

Simplify the expression

More Steps

Evaluate

\frac{25}{2}

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

\frac{25}{2}

Simplify the radical expression

\frac{5}{2}

Multiply by the Conjugate

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

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

\frac{5 2}{2}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

x_{1} \approx - 3.535534, x_{2} = 0, x_{3} \approx 3.535534

Show Solution