Solve (2x^(2)-9x^2)^(2)-4

Question

(2 x^{2} - 9 x^{2})^{2} - 4

Simplify the expression

49 x^{4} - 4

Show Solution

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

Show Solution

x_{1} = - \frac{14}{7}, x_{2} = \frac{14}{7}

Alternative Form

x_{1} \approx - 0.534522, x_{2} \approx 0.534522

Evaluate

(2 x^{2} - 9 x^{2})^{2} - 4

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

(2 x^{2} - 9 x^{2})^{2} - 4 = 0

Subtract the terms

More Steps

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

Rewrite the expression

More Steps

49 x^{4} - 4 = 0

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

49 x^{4} = 0 + 4

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

49 x^{4} = 4

Divide both sides

\frac{49 x ^{4}}{49} = \frac{4}{49}

Divide the numbers

x^{4} = \frac{4}{49}

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

x = \pm 4 \frac{4}{49}

Simplify the expression

More Steps

x = \pm \frac{14}{7}

Separate the equation into 2 possible cases

x = \frac{14}{7} x = - \frac{14}{7}

Solution

x_{1} = - \frac{14}{7}, x_{2} = \frac{14}{7}

Alternative Form

x_{1} \approx - 0.534522, x_{2} \approx 0.534522

Show Solution