Solve 14x^2 - 16x^4

Question

Factor the expression

2 x^{2} (7 - 8 x^{2})

Evaluate

14 x^{2} - 16 x^{4}

Rewrite the expression

2 x^{2} \times 7 - 2 x^{2} \times 8 x^{2}

Solution

2 x^{2} (7 - 8 x^{2})

Show Solution

x_{1} = - \frac{14}{4}, x_{2} = 0, x_{3} = \frac{14}{4}

Alternative Form

x_{1} \approx - 0.935414, x_{2} = 0, x_{3} \approx 0.935414

Evaluate

14 x^{2} - 16 x^{4}

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

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

Factor the expression

2 x^{2} (7 - 8 x^{2}) = 0

Divide both sides

x^{2} (7 - 8 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 7 - 8 x^{2} = 0

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

x = 0 7 - 8 x^{2} = 0

Solve the equation

More Steps

Evaluate

7 - 8 x^{2} = 0

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

- 8 x^{2} = 0 - 7

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

- 8 x^{2} = - 7

Change the signs on both sides of the equation

8 x^{2} = 7

Divide both sides

\frac{8 x ^{2}}{8} = \frac{7}{8}

Divide the numbers

x^{2} = \frac{7}{8}

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

x = \pm \frac{7}{8}

Simplify the expression

More Steps

Evaluate

\frac{7}{8}

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

\frac{7}{8}

Simplify the radical expression

\frac{7}{2 2}

Multiply by the Conjugate

\frac{7 \times 2}{2 2 \times 2}

Multiply the numbers

\frac{14}{2 2 \times 2}

Multiply the numbers

\frac{14}{4}

x = \pm \frac{14}{4}

Separate the equation into 2 possible cases

x = \frac{14}{4} x = - \frac{14}{4}

x = 0 x = \frac{14}{4} x = - \frac{14}{4}

Solution

x_{1} = - \frac{14}{4}, x_{2} = 0, x_{3} = \frac{14}{4}

Alternative Form

x_{1} \approx - 0.935414, x_{2} = 0, x_{3} \approx 0.935414

Show Solution