Solve 3x^2-x 75x^2-2x^2

Question

Simplify the expression

x^{2} - 75 x^{3}

Evaluate

3 x^{2} - x \times 75 x^{2} - 2 x^{2}

Multiply

More Steps

Multiply the terms

- x \times 75 x^{2}

Multiply the terms with the same base by adding their exponents

- x^{1 + 2} \times 75

Add the numbers

- x^{3} \times 75

Use the commutative property to reorder the terms

- 75 x^{3}

3 x^{2} - 75 x^{3} - 2 x^{2}

Solution

More Steps

Evaluate

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

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

(3 - 2) x^{2}

Subtract the numbers

x^{2}

x^{2} - 75 x^{3}

Show Solution

Factor the expression

x^{2} (1 - 75 x)

Evaluate

3 x^{2} - x \times 75 x^{2} - 2 x^{2}

Multiply

More Steps

Multiply the terms

x \times 75 x^{2}

Multiply the terms with the same base by adding their exponents

x^{1 + 2} \times 75

Add the numbers

x^{3} \times 75

Use the commutative property to reorder the terms

75 x^{3}

3 x^{2} - 75 x^{3} - 2 x^{2}

Subtract the terms

More Steps

Evaluate

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

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

(3 - 2) x^{2}

Subtract the numbers

x^{2}

x^{2} - 75 x^{3}

Rewrite the expression

x^{2} - x^{2} \times 75 x

Solution

x^{2} (1 - 75 x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{75}

Alternative Form

x_{1} = 0, x_{2} = 0.01 \dot{3}

Evaluate

3 x^{2} - x \times 75 x^{2} - 2 x^{2}

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

3 x^{2} - x \times 75 x^{2} - 2 x^{2} = 0

Multiply

More Steps

Multiply the terms

x \times 75 x^{2}

Multiply the terms with the same base by adding their exponents

x^{1 + 2} \times 75

Add the numbers

x^{3} \times 75

Use the commutative property to reorder the terms

75 x^{3}

3 x^{2} - 75 x^{3} - 2 x^{2} = 0

Subtract the terms

More Steps

Simplify

3 x^{2} - 75 x^{3} - 2 x^{2}

Subtract the terms

More Steps

Evaluate

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

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

(3 - 2) x^{2}

Subtract the numbers

x^{2}

x^{2} - 75 x^{3}

x^{2} - 75 x^{3} = 0

Factor the expression

x^{2} (1 - 75 x) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 75 x = 0

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

x = 0 1 - 75 x = 0

Solve the equation

More Steps

Evaluate

1 - 75 x = 0

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

- 75 x = 0 - 1

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

- 75 x = - 1

Change the signs on both sides of the equation

75 x = 1

Divide both sides

\frac{75 x}{75} = \frac{1}{75}

Divide the numbers

x = \frac{1}{75}

x = 0 x = \frac{1}{75}

Solution

x_{1} = 0, x_{2} = \frac{1}{75}

Alternative Form

x_{1} = 0, x_{2} = 0.01 \dot{3}

Show Solution