Solve (5x^2 4x) - (3x^1-2x)

Question

Simplify the expression

20 x^{3} - x

Evaluate

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

Multiply

More Steps

Multiply the terms

5 x^{2} \times 4 x

Multiply the terms

20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

20 x^{2 + 1}

Add the numbers

20 x^{3}

20 x^{3} - (3 x - 2 x)

Solution

More Steps

Simplify

3 x - 2 x

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

(3 - 2) x

Subtract the numbers

x

20 x^{3} - x

Show Solution

Factor the expression

x (20 x^{2} - 1)

Evaluate

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

Multiply

More Steps

Multiply the terms

5 x^{2} \times 4 x

Multiply the terms

20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

20 x^{2 + 1}

Add the numbers

20 x^{3}

20 x^{3} - (3 x - 2 x)

Subtract the terms

More Steps

Simplify

3 x - 2 x

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

(3 - 2) x

Subtract the numbers

x

20 x^{3} - x

Rewrite the expression

x \times 20 x^{2} - x

Solution

x (20 x^{2} - 1)

Show Solution

Find the roots

x_{1} = - \frac{5}{10}, x_{2} = 0, x_{3} = \frac{5}{10}

Alternative Form

x_{1} \approx - 0.223607, x_{2} = 0, x_{3} \approx 0.223607

Evaluate

(5 x^{2} \times 4 x) - (3 x^{1} - 2 x)

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

(5 x^{2} \times 4 x) - (3 x^{1} - 2 x) = 0

Multiply

More Steps

Multiply the terms

5 x^{2} \times 4 x

Multiply the terms

20 x^{2} \times x

Multiply the terms with the same base by adding their exponents

20 x^{2 + 1}

Add the numbers

20 x^{3}

20 x^{3} - (3 x^{1} - 2 x) = 0

Evaluate the power

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

Subtract the terms

More Steps

Simplify

3 x - 2 x

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

(3 - 2) x

Subtract the numbers

x

20 x^{3} - x = 0

Factor the expression

x (20 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x = 0 20 x^{2} - 1 = 0

Solve the equation

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Evaluate

20 x^{2} - 1 = 0

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

20 x^{2} = 0 + 1

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

20 x^{2} = 1

Divide both sides

\frac{20 x ^{2}}{20} = \frac{1}{20}

Divide the numbers

x^{2} = \frac{1}{20}

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

x = \pm \frac{1}{20}

Simplify the expression

More Steps

Evaluate

\frac{1}{20}

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

\frac{1}{20}

Simplify the radical expression

\frac{1}{20}

Simplify the radical expression

\frac{1}{2 5}

Multiply by the Conjugate

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

Multiply the numbers

\frac{5}{10}

x = \pm \frac{5}{10}

Separate the equation into 2 possible cases

x = \frac{5}{10} x = - \frac{5}{10}

x = 0 x = \frac{5}{10} x = - \frac{5}{10}

Solution

x_{1} = - \frac{5}{10}, x_{2} = 0, x_{3} = \frac{5}{10}

Alternative Form

x_{1} \approx - 0.223607, x_{2} = 0, x_{3} \approx 0.223607

Show Solution