Solve 2x^2 - 6x^4x^2 12x - x^2

Question

Simplify the expression

x^{2} - 72 x^{7}

Evaluate

2 x^{2} - 6 x^{4} \times x^{2} \times 12 x - x^{2}

Multiply

More Steps

Multiply the terms

- 6 x^{4} \times x^{2} \times 12 x

Multiply the terms

- 72 x^{4} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

- 72 x^{4 + 2 + 1}

Add the numbers

- 72 x^{7}

2 x^{2} - 72 x^{7} - x^{2}

Solution

More Steps

Evaluate

2 x^{2} - x^{2}

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

(2 - 1) x^{2}

Subtract the numbers

x^{2}

x^{2} - 72 x^{7}

Show Solution

Factor the expression

x^{2} (1 - 72 x^{5})

Evaluate

2 x^{2} - 6 x^{4} \times x^{2} \times 12 x - x^{2}

Multiply

More Steps

Multiply the terms

6 x^{4} \times x^{2} \times 12 x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

72 x^{4 + 2 + 1}

Add the numbers

72 x^{7}

2 x^{2} - 72 x^{7} - x^{2}

Subtract the terms

More Steps

Evaluate

2 x^{2} - x^{2}

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

(2 - 1) x^{2}

Subtract the numbers

x^{2}

x^{2} - 72 x^{7}

Rewrite the expression

x^{2} - x^{2} \times 72 x^{5}

Solution

x^{2} (1 - 72 x^{5})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5 7 2 ^{4}}{72}

Alternative Form

x_{1} = 0, x_{2} \approx 0.425142

Evaluate

2 x^{2} - 6 x^{4} \times x^{2} \times 12 x - x^{2}

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

2 x^{2} - 6 x^{4} \times x^{2} \times 12 x - x^{2} = 0

Multiply

More Steps

Multiply the terms

6 x^{4} \times x^{2} \times 12 x

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

72 x^{4 + 2 + 1}

Add the numbers

72 x^{7}

2 x^{2} - 72 x^{7} - x^{2} = 0

Subtract the terms

More Steps

Simplify

2 x^{2} - 72 x^{7} - x^{2}

Subtract the terms

More Steps

Evaluate

2 x^{2} - x^{2}

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

(2 - 1) x^{2}

Subtract the numbers

x^{2}

x^{2} - 72 x^{7}

x^{2} - 72 x^{7} = 0

Factor the expression

x^{2} (1 - 72 x^{5}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 72 x^{5} = 0

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

x = 0 1 - 72 x^{5} = 0

Solve the equation

More Steps

Evaluate

1 - 72 x^{5} = 0

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

- 72 x^{5} = 0 - 1

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

- 72 x^{5} = - 1

Change the signs on both sides of the equation

72 x^{5} = 1

Divide both sides

\frac{72 x ^{5}}{72} = \frac{1}{72}

Divide the numbers

x^{5} = \frac{1}{72}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{72}

Calculate

x = 5 \frac{1}{72}

Simplify the root

More Steps

Evaluate

5 \frac{1}{72}

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

\frac{5 1}{5 72}

Simplify the radical expression

\frac{1}{5 72}

Multiply by the Conjugate

\frac{5 7 2 ^{4}}{5 72 \times 5 7 2 ^{4}}

Multiply the numbers

\frac{5 7 2 ^{4}}{72}

x = \frac{5 7 2 ^{4}}{72}

x = 0 x = \frac{5 7 2 ^{4}}{72}

Solution

x_{1} = 0, x_{2} = \frac{5 7 2 ^{4}}{72}

Alternative Form

x_{1} = 0, x_{2} \approx 0.425142

Show Solution