Solve (2x^25)(2x^2 - 5)

Question

Simplify the expression

20 x^{4} - 50 x^{2}

Evaluate

(2 x^{2} \times 5) (2 x^{2} - 5)

Remove the parentheses

2 x^{2} \times 5 (2 x^{2} - 5)

Multiply the terms

10 x^{2} (2 x^{2} - 5)

Apply the distributive property

10 x^{2} \times 2 x^{2} - 10 x^{2} \times 5

Multiply the terms

More Steps

Evaluate

10 x^{2} \times 2 x^{2}

Multiply the numbers

20 x^{2} \times x^{2}

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 2}

Add the numbers

x^{4}

20 x^{4}

20 x^{4} - 10 x^{2} \times 5

Solution

20 x^{4} - 50 x^{2}

Show Solution

x_{1} = - \frac{10}{2}, x_{2} = 0, x_{3} = \frac{10}{2}

Alternative Form

x_{1} \approx - 1.581139, x_{2} = 0, x_{3} \approx 1.581139

Evaluate

(2 x^{2} \times 5) (2 x^{2} - 5)

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

(2 x^{2} \times 5) (2 x^{2} - 5) = 0

Multiply the terms

10 x^{2} (2 x^{2} - 5) = 0

Elimination the left coefficient

x^{2} (2 x^{2} - 5) = 0

Separate the equation into 2 possible cases

x^{2} = 0 2 x^{2} - 5 = 0

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

x = 0 2 x^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 5 = 0

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

2 x^{2} = 0 + 5

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

2 x^{2} = 5

Divide both sides

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

Divide the numbers

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{5}{2}

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

\frac{5}{2}

Multiply by the Conjugate

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

Multiply the numbers

\frac{10}{2 \times 2}

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

\frac{10}{2}

x = \pm \frac{10}{2}

Separate the equation into 2 possible cases

x = \frac{10}{2} x = - \frac{10}{2}

x = 0 x = \frac{10}{2} x = - \frac{10}{2}

Solution

x_{1} = - \frac{10}{2}, x_{2} = 0, x_{3} = \frac{10}{2}

Alternative Form

x_{1} \approx - 1.581139, x_{2} = 0, x_{3} \approx 1.581139

Show Solution