Solve 9m^2 - 7m^4 = 0

Question

Solve the equation

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

Alternative Form

m_{1} \approx - 1.133893, m_{2} = 0, m_{3} \approx 1.133893

Evaluate

9 m^{2} - 7 m^{4} = 0

Factor the expression

m^{2} (9 - 7 m^{2}) = 0

Separate the equation into 2 possible cases

m^{2} = 0 9 - 7 m^{2} = 0

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

m = 0 9 - 7 m^{2} = 0

Solve the equation

More Steps

Evaluate

9 - 7 m^{2} = 0

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

- 7 m^{2} = 0 - 9

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

- 7 m^{2} = - 9

Change the signs on both sides of the equation

7 m^{2} = 9

Divide both sides

\frac{7 m ^{2}}{7} = \frac{9}{7}

Divide the numbers

m^{2} = \frac{9}{7}

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

m = \pm \frac{9}{7}

Simplify the expression

More Steps

Evaluate

\frac{9}{7}

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

\frac{9}{7}

Simplify the radical expression

\frac{3}{7}

Multiply by the Conjugate

\frac{3 7}{7 \times 7}

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

\frac{3 7}{7}

m = \pm \frac{3 7}{7}

Separate the equation into 2 possible cases

m = \frac{3 7}{7} m = - \frac{3 7}{7}

m = 0 m = \frac{3 7}{7} m = - \frac{3 7}{7}

Solution

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

Alternative Form

m_{1} \approx - 1.133893, m_{2} = 0, m_{3} \approx 1.133893

Show Solution