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

Question

Simplify the expression

20 x^{3} - 3 x^{2} + 2 x

Evaluate

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

Solution

20 x^{3} - 3 x^{2} + 2 x

Show Solution

Factor the expression

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

Evaluate

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

20 x^{3} - 3 x^{2} + 2 x

Rewrite the expression

x \times 20 x^{2} - x \times 3 x + x \times 2

Solution

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

Show Solution

Find the roots

x_{1} = \frac{3}{40} - \frac{151}{40} i, x_{2} = \frac{3}{40} + \frac{151}{40} i, x_{3} = 0

Alternative Form

x_{1} \approx 0.075 - 0.307205 i, x_{2} \approx 0.075 + 0.307205 i, x_{3} = 0

Evaluate

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

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

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

20 x^{3} - 3 x^{2} + 2 x = 0

Factor the expression

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

Separate the equation into 2 possible cases

x = 0 20 x^{2} - 3 x + 2 = 0

Solve the equation

More Steps

Evaluate

20 x^{2} - 3 x + 2 = 0

Substitute a= 20,b= - 3 and c= 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 20 \times 2}{2 \times 20}

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 20 \times 2}{40}

Simplify the expression

More Steps

Evaluate

(- 3)^{2} - 4 \times 20 \times 2

Multiply the terms

(- 3)^{2} - 160

Rewrite the expression

3^{2} - 160

Evaluate the power

9 - 160

Subtract the numbers

- 151

x = \frac{3 \pm - 151}{40}

Simplify the radical expression

More Steps

Evaluate

- 151

Evaluate the power

151 \times - 1

Evaluate the power

151 \times i

x = \frac{3 \pm 151 \times i}{40}

Separate the equation into 2 possible cases

x = \frac{3 + 151 \times i}{40} x = \frac{3 - 151 \times i}{40}

Simplify the expression

x = \frac{3}{40} + \frac{151}{40} i x = \frac{3 - 151 \times i}{40}

Simplify the expression

x = \frac{3}{40} + \frac{151}{40} i x = \frac{3}{40} - \frac{151}{40} i

x = 0 x = \frac{3}{40} + \frac{151}{40} i x = \frac{3}{40} - \frac{151}{40} i

Solution

x_{1} = \frac{3}{40} - \frac{151}{40} i, x_{2} = \frac{3}{40} + \frac{151}{40} i, x_{3} = 0

Alternative Form

x_{1} \approx 0.075 - 0.307205 i, x_{2} \approx 0.075 + 0.307205 i, x_{3} = 0

Show Solution