Solve 16x^(2)-(3x^2)^(2)=0

Question

Solve the equation

x_{1} = - \frac{4}{3}, x_{2} = 0, x_{3} = \frac{4}{3}

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 0, x_{3} = 1. \dot{3}

Evaluate

16 x^{2} - (3 x^{2})^{2} = 0

Rewrite the expression

More Steps

Evaluate

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

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

3^{2} (x^{2})^{2}

Evaluate the power

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

Evaluate the power

More Steps

Evaluate

(x^{2})^{2}

Multiply the exponents

x^{2 \times 2}

Multiply the terms

x^{4}

9 x^{4}

16 x^{2} - 9 x^{4} = 0

Factor the expression

x^{2} (16 - 9 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 16 - 9 x^{2} = 0

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

x = 0 16 - 9 x^{2} = 0

Solve the equation

More Steps

Evaluate

16 - 9 x^{2} = 0

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

- 9 x^{2} = 0 - 16

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

- 9 x^{2} = - 16

Change the signs on both sides of the equation

9 x^{2} = 16

Divide both sides

\frac{9 x ^{2}}{9} = \frac{16}{9}

Divide the numbers

x^{2} = \frac{16}{9}

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

x = \pm \frac{16}{9}

Simplify the expression

More Steps

Evaluate

\frac{16}{9}

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

\frac{16}{9}

Simplify the radical expression

\frac{4}{9}

Simplify the radical expression

\frac{4}{3}

x = \pm \frac{4}{3}

Separate the equation into 2 possible cases

x = \frac{4}{3} x = - \frac{4}{3}

x = 0 x = \frac{4}{3} x = - \frac{4}{3}

Solution

x_{1} = - \frac{4}{3}, x_{2} = 0, x_{3} = \frac{4}{3}

Alternative Form

x_{1} = - 1. \dot{3}, x_{2} = 0, x_{3} = 1. \dot{3}

Show Solution