Solve (2x 7)^2 = 9 ( x^2)^2

Question

Solve the equation

x_{1} = - \frac{14}{3}, x_{2} = 0, x_{3} = \frac{14}{3}

Alternative Form

x_{1} = - 4. \dot{6}, x_{2} = 0, x_{3} = 4. \dot{6}

Evaluate

(2 x \times 7)^{2} = 9 (x^{2})^{2}

Simplify

More Steps

Evaluate

(2 x \times 7)^{2}

Multiply the terms

(14 x)^{2}

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

1 4^{2} x^{2}

Evaluate the power

196 x^{2}

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

Simplify

More Steps

Evaluate

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

Multiply the exponents

9 x^{2 \times 2}

Multiply the numbers

9 x^{4}

196 x^{2} = 9 x^{4}

Add or subtract both sides

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

Factor the expression

x^{2} (196 - 9 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 196 - 9 x^{2} = 0

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

x = 0 196 - 9 x^{2} = 0

Solve the equation

More Steps

Evaluate

196 - 9 x^{2} = 0

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

- 9 x^{2} = 0 - 196

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

- 9 x^{2} = - 196

Change the signs on both sides of the equation

9 x^{2} = 196

Divide both sides

\frac{9 x ^{2}}{9} = \frac{196}{9}

Divide the numbers

x^{2} = \frac{196}{9}

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

x = \pm \frac{196}{9}

Simplify the expression

More Steps

Evaluate

\frac{196}{9}

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

\frac{196}{9}

Simplify the radical expression

\frac{14}{9}

Simplify the radical expression

\frac{14}{3}

x = \pm \frac{14}{3}

Separate the equation into 2 possible cases

x = \frac{14}{3} x = - \frac{14}{3}

x = 0 x = \frac{14}{3} x = - \frac{14}{3}

Solution

x_{1} = - \frac{14}{3}, x_{2} = 0, x_{3} = \frac{14}{3}

Alternative Form

x_{1} = - 4. \dot{6}, x_{2} = 0, x_{3} = 4. \dot{6}

Show Solution