Solve 12x^(2)-16x^(2) 7x^(2)

Question

Simplify the expression

12 x^{2} - 112 x^{4}

Evaluate

12 x^{2} - 16 x^{2} \times 7 x^{2}

Solution

More Steps

Evaluate

16 x^{2} \times 7 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

112 x^{2 + 2}

Add the numbers

112 x^{4}

12 x^{2} - 112 x^{4}

Show Solution

Factor the expression

4 x^{2} (3 - 28 x^{2})

Evaluate

12 x^{2} - 16 x^{2} \times 7 x^{2}

Multiply

More Steps

Evaluate

16 x^{2} \times 7 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

112 x^{2 + 2}

Add the numbers

112 x^{4}

12 x^{2} - 112 x^{4}

Rewrite the expression

4 x^{2} \times 3 - 4 x^{2} \times 28 x^{2}

Solution

4 x^{2} (3 - 28 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{21}{14}, x_{2} = 0, x_{3} = \frac{21}{14}

Alternative Form

x_{1} \approx - 0.327327, x_{2} = 0, x_{3} \approx 0.327327

Evaluate

12 x^{2} - 16 x^{2} \times 7 x^{2}

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

12 x^{2} - 16 x^{2} \times 7 x^{2} = 0

Multiply

More Steps

Multiply the terms

16 x^{2} \times 7 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

112 x^{2 + 2}

Add the numbers

112 x^{4}

12 x^{2} - 112 x^{4} = 0

Factor the expression

4 x^{2} (3 - 28 x^{2}) = 0

Divide both sides

x^{2} (3 - 28 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 - 28 x^{2} = 0

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

x = 0 3 - 28 x^{2} = 0

Solve the equation

More Steps

Evaluate

3 - 28 x^{2} = 0

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

- 28 x^{2} = 0 - 3

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

- 28 x^{2} = - 3

Change the signs on both sides of the equation

28 x^{2} = 3

Divide both sides

\frac{28 x ^{2}}{28} = \frac{3}{28}

Divide the numbers

x^{2} = \frac{3}{28}

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

x = \pm \frac{3}{28}

Simplify the expression

More Steps

Evaluate

\frac{3}{28}

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

\frac{3}{28}

Simplify the radical expression

\frac{3}{2 7}

Multiply by the Conjugate

\frac{3 \times 7}{2 7 \times 7}

Multiply the numbers

\frac{21}{2 7 \times 7}

Multiply the numbers

\frac{21}{14}

x = \pm \frac{21}{14}

Separate the equation into 2 possible cases

x = \frac{21}{14} x = - \frac{21}{14}

x = 0 x = \frac{21}{14} x = - \frac{21}{14}

Solution

x_{1} = - \frac{21}{14}, x_{2} = 0, x_{3} = \frac{21}{14}

Alternative Form

x_{1} \approx - 0.327327, x_{2} = 0, x_{3} \approx 0.327327

Show Solution