Solve 3x ^ 2 4x ^ 2 - 5x ^ 2

Question

Simplify the expression

12 x^{4} - 5 x^{2}

Evaluate

3 x^{2} \times 4 x^{2} - 5 x^{2}

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{2 + 2}

Add the numbers

12 x^{4}

12 x^{4} - 5 x^{2}

Show Solution

Factor the expression

x^{2} (12 x^{2} - 5)

Evaluate

3 x^{2} \times 4 x^{2} - 5 x^{2}

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{2 + 2}

Add the numbers

12 x^{4}

12 x^{4} - 5 x^{2}

Rewrite the expression

x^{2} \times 12 x^{2} - x^{2} \times 5

Solution

x^{2} (12 x^{2} - 5)

Show Solution

Find the roots

x_{1} = - \frac{15}{6}, x_{2} = 0, x_{3} = \frac{15}{6}

Alternative Form

x_{1} \approx - 0.645497, x_{2} = 0, x_{3} \approx 0.645497

Evaluate

3 x^{2} \times 4 x^{2} - 5 x^{2}

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

3 x^{2} \times 4 x^{2} - 5 x^{2} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

12 x^{2 + 2}

Add the numbers

12 x^{4}

12 x^{4} - 5 x^{2} = 0

Factor the expression

x^{2} (12 x^{2} - 5) = 0

Separate the equation into 2 possible cases

x^{2} = 0 12 x^{2} - 5 = 0

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

x = 0 12 x^{2} - 5 = 0

Solve the equation

More Steps

Evaluate

12 x^{2} - 5 = 0

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

12 x^{2} = 0 + 5

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

12 x^{2} = 5

Divide both sides

\frac{12 x ^{2}}{12} = \frac{5}{12}

Divide the numbers

x^{2} = \frac{5}{12}

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

x = \pm \frac{5}{12}

Simplify the expression

More Steps

Evaluate

\frac{5}{12}

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

\frac{5}{12}

Simplify the radical expression

\frac{5}{2 3}

Multiply by the Conjugate

\frac{5 \times 3}{2 3 \times 3}

Multiply the numbers

\frac{15}{2 3 \times 3}

Multiply the numbers

\frac{15}{6}

x = \pm \frac{15}{6}

Separate the equation into 2 possible cases

x = \frac{15}{6} x = - \frac{15}{6}

x = 0 x = \frac{15}{6} x = - \frac{15}{6}

Solution

x_{1} = - \frac{15}{6}, x_{2} = 0, x_{3} = \frac{15}{6}

Alternative Form

x_{1} \approx - 0.645497, x_{2} = 0, x_{3} \approx 0.645497

Show Solution