Solve (2x^(2)-10x^4)-(-2x^2)^(2)

Question

Simplify the expression

2 x^{2} - 14 x^{4}

Evaluate

(2 x^{2} - 10 x^{4}) - (- 2 x^{2})^{2}

Remove the parentheses

2 x^{2} - 10 x^{4} - (- 2 x^{2})^{2}

Rewrite the expression

2 x^{2} - 10 x^{4} - 4 x^{4}

Solution

More Steps

Evaluate

- 10 x^{4} - 4 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- 10 - 4) x^{4}

Subtract the numbers

- 14 x^{4}

2 x^{2} - 14 x^{4}

Show Solution

Factor the expression

2 x^{2} (1 - 7 x^{2})

Evaluate

(2 x^{2} - 10 x^{4}) - (- 2 x^{2})^{2}

Remove the parentheses

2 x^{2} - 10 x^{4} - (- 2 x^{2})^{2}

Rewrite the expression

2 x^{2} (1 - 5 x^{2}) - 2 x^{2} \times 2 x^{2}

Factor out 2 x^{2} from the expression

2 x^{2} (1 - 5 x^{2} - 2 x^{2})

Solution

2 x^{2} (1 - 7 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{7}{7}, x_{2} = 0, x_{3} = \frac{7}{7}

Alternative Form

x_{1} \approx - 0.377964, x_{2} = 0, x_{3} \approx 0.377964

Evaluate

(2 x^{2} - 10 x^{4}) - (- 2 x^{2})^{2}

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

(2 x^{2} - 10 x^{4}) - (- 2 x^{2})^{2} = 0

Remove the parentheses

2 x^{2} - 10 x^{4} - (- 2 x^{2})^{2} = 0

Subtract the terms

More Steps

Simplify

2 x^{2} - 10 x^{4} - (- 2 x^{2})^{2}

Rewrite the expression

More Steps

Evaluate

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

Determine the sign

(2 x^{2})^{2}

To raise a product to a power,raise each factor to that power

2^{2} (x^{2})^{2}

Evaluate the power

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

Evaluate the power

4 x^{4}

2 x^{2} - 10 x^{4} - 4 x^{4}

Subtract the terms

More Steps

Evaluate

- 10 x^{4} - 4 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- 10 - 4) x^{4}

Subtract the numbers

- 14 x^{4}

2 x^{2} - 14 x^{4}

2 x^{2} - 14 x^{4} = 0

Factor the expression

2 x^{2} (1 - 7 x^{2}) = 0

Divide both sides

x^{2} (1 - 7 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 7 x^{2} = 0

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

x = 0 1 - 7 x^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 7 x^{2} = 0

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

- 7 x^{2} = 0 - 1

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

- 7 x^{2} = - 1

Change the signs on both sides of the equation

7 x^{2} = 1

Divide both sides

\frac{7 x ^{2}}{7} = \frac{1}{7}

Divide the numbers

x^{2} = \frac{1}{7}

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

x = \pm \frac{1}{7}

Simplify the expression

More Steps

Evaluate

\frac{1}{7}

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

\frac{1}{7}

Simplify the radical expression

\frac{1}{7}

Multiply by the Conjugate

\frac{7}{7 \times 7}

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

\frac{7}{7}

x = \pm \frac{7}{7}

Separate the equation into 2 possible cases

x = \frac{7}{7} x = - \frac{7}{7}

x = 0 x = \frac{7}{7} x = - \frac{7}{7}

Solution

x_{1} = - \frac{7}{7}, x_{2} = 0, x_{3} = \frac{7}{7}

Alternative Form

x_{1} \approx - 0.377964, x_{2} = 0, x_{3} \approx 0.377964

Show Solution