Solve 3x^(2)-7x^(2) 12x^(2)-5x^(2)

Question

Simplify the expression

- 2 x^{2} - 84 x^{4}

Evaluate

3 x^{2} - 7 x^{2} \times 12 x^{2} - 5 x^{2}

Multiply

More Steps

Multiply the terms

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

Multiply the terms

- 84 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 84 x^{2 + 2}

Add the numbers

- 84 x^{4}

3 x^{2} - 84 x^{4} - 5 x^{2}

Solution

More Steps

Evaluate

3 x^{2} - 5 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(3 - 5) x^{2}

Subtract the numbers

- 2 x^{2}

- 2 x^{2} - 84 x^{4}

Show Solution

Factor the expression

- 2 x^{2} (1 + 42 x^{2})

Evaluate

3 x^{2} - 7 x^{2} \times 12 x^{2} - 5 x^{2}

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

84 x^{2 + 2}

Add the numbers

84 x^{4}

3 x^{2} - 84 x^{4} - 5 x^{2}

Subtract the terms

More Steps

Evaluate

3 x^{2} - 5 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(3 - 5) x^{2}

Subtract the numbers

- 2 x^{2}

- 2 x^{2} - 84 x^{4}

Rewrite the expression

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

Solution

- 2 x^{2} (1 + 42 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{42}{42} i, x_{2} = \frac{42}{42} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.154303 i, x_{2} \approx 0.154303 i, x_{3} = 0

Evaluate

3 x^{2} - 7 x^{2} \times 12 x^{2} - 5 x^{2}

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

3 x^{2} - 7 x^{2} \times 12 x^{2} - 5 x^{2} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

84 x^{2 + 2}

Add the numbers

84 x^{4}

3 x^{2} - 84 x^{4} - 5 x^{2} = 0

Subtract the terms

More Steps

Simplify

3 x^{2} - 84 x^{4} - 5 x^{2}

Subtract the terms

More Steps

Evaluate

3 x^{2} - 5 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(3 - 5) x^{2}

Subtract the numbers

- 2 x^{2}

- 2 x^{2} - 84 x^{4}

- 2 x^{2} - 84 x^{4} = 0

Factor the expression

- 2 x^{2} (1 + 42 x^{2}) = 0

Divide both sides

x^{2} (1 + 42 x^{2}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 + 42 x^{2} = 0

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

x = 0 1 + 42 x^{2} = 0

Solve the equation

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Evaluate

1 + 42 x^{2} = 0

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

42 x^{2} = 0 - 1

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

42 x^{2} = - 1

Divide both sides

\frac{42 x ^{2}}{42} = \frac{- 1}{42}

Divide the numbers

x^{2} = \frac{- 1}{42}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{2} = - \frac{1}{42}

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

x = \pm - \frac{1}{42}

Simplify the expression

More Steps

Evaluate

- \frac{1}{42}

Evaluate the power

\frac{1}{42} \times - 1

Evaluate the power

\frac{1}{42} \times i

Evaluate the power

\frac{42}{42} i

x = \pm \frac{42}{42} i

Separate the equation into 2 possible cases

x = \frac{42}{42} i x = - \frac{42}{42} i

x = 0 x = \frac{42}{42} i x = - \frac{42}{42} i

Solution

x_{1} = - \frac{42}{42} i, x_{2} = \frac{42}{42} i, x_{3} = 0

Alternative Form

x_{1} \approx - 0.154303 i, x_{2} \approx 0.154303 i, x_{3} = 0

Show Solution