Solve 9x^2(3x^2 14-8)

Question

Simplify the expression

378 x^{4} - 72 x^{2}

Evaluate

9 x^{2} (3 x^{2} \times 14 - 8)

Multiply the terms

9 x^{2} (42 x^{2} - 8)

Apply the distributive property

9 x^{2} \times 42 x^{2} - 9 x^{2} \times 8

Multiply the terms

More Steps

Evaluate

9 x^{2} \times 42 x^{2}

Multiply the numbers

378 x^{2} \times x^{2}

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 2}

Add the numbers

x^{4}

378 x^{4}

378 x^{4} - 9 x^{2} \times 8

Solution

378 x^{4} - 72 x^{2}

Show Solution

18 x^{2} (21 x^{2} - 4)

Evaluate

9 x^{2} (3 x^{2} \times 14 - 8)

Multiply the terms

9 x^{2} (42 x^{2} - 8)

Factor the expression

9 x^{2} \times 2 (21 x^{2} - 4)

Solution

18 x^{2} (21 x^{2} - 4)

Show Solution

x_{1} = - \frac{2 21}{21}, x_{2} = 0, x_{3} = \frac{2 21}{21}

Alternative Form

x_{1} \approx - 0.436436, x_{2} = 0, x_{3} \approx 0.436436

Evaluate

9 x^{2} (3 x^{2} \times 14 - 8)

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

9 x^{2} (3 x^{2} \times 14 - 8) = 0

Multiply the terms

9 x^{2} (42 x^{2} - 8) = 0

Elimination the left coefficient

x^{2} (42 x^{2} - 8) = 0

Separate the equation into 2 possible cases

x^{2} = 0 42 x^{2} - 8 = 0

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

x = 0 42 x^{2} - 8 = 0

Solve the equation

More Steps

Evaluate

42 x^{2} - 8 = 0

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

42 x^{2} = 0 + 8

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

42 x^{2} = 8

Divide both sides

\frac{42 x ^{2}}{42} = \frac{8}{42}

Divide the numbers

x^{2} = \frac{8}{42}

Cancel out the common factor 2

x^{2} = \frac{4}{21}

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

x = \pm \frac{4}{21}

Simplify the expression

More Steps

Evaluate

\frac{4}{21}

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

\frac{4}{21}

Simplify the radical expression

\frac{2}{21}

Multiply by the Conjugate

\frac{2 21}{21 \times 21}

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

\frac{2 21}{21}

x = \pm \frac{2 21}{21}

Separate the equation into 2 possible cases

x = \frac{2 21}{21} x = - \frac{2 21}{21}

x = 0 x = \frac{2 21}{21} x = - \frac{2 21}{21}

Solution

x_{1} = - \frac{2 21}{21}, x_{2} = 0, x_{3} = \frac{2 21}{21}

Alternative Form

x_{1} \approx - 0.436436, x_{2} = 0, x_{3} \approx 0.436436

Show Solution