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

Question

Simplify the expression

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

Evaluate

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

Multiply

More Steps

Multiply the terms

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

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

Solution

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

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Factor the expression

x (10 x^{2} - 3 x + 1)

Evaluate

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

Multiply

More Steps

Multiply the terms

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

10 x^{3} - (3 x^{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

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

Rewrite the expression

x \times 10 x^{2} - x \times 3 x + x

Solution

x (10 x^{2} - 3 x + 1)

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Find the roots

x_{1} = \frac{3}{20} - \frac{31}{20} i, x_{2} = \frac{3}{20} + \frac{31}{20} i, x_{3} = 0

Alternative Form

x_{1} \approx 0.15 - 0.278388 i, x_{2} \approx 0.15 + 0.278388 i, x_{3} = 0

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

5 x^{2} \times 2 x

Multiply the terms

10 x^{2} \times x

Multiply the terms with the same base by adding their exponents

10 x^{2 + 1}

Add the numbers

10 x^{3}

10 x^{3} - (3 x^{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

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

Factor the expression

x (10 x^{2} - 3 x + 1) = 0

Separate the equation into 2 possible cases

x = 0 10 x^{2} - 3 x + 1 = 0

Solve the equation

More Steps

Evaluate

10 x^{2} - 3 x + 1 = 0

Substitute a= 10,b= - 3 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 10}{2 \times 10}

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 10}{20}

Simplify the expression

More Steps

Evaluate

(- 3)^{2} - 4 \times 10

Multiply the numbers

(- 3)^{2} - 40

Rewrite the expression

3^{2} - 40

Evaluate the power

9 - 40

Subtract the numbers

- 31

x = \frac{3 \pm - 31}{20}

Simplify the radical expression

More Steps

Evaluate

- 31

Evaluate the power

31 \times - 1

Evaluate the power

31 \times i

x = \frac{3 \pm 31 \times i}{20}

Separate the equation into 2 possible cases

x = \frac{3 + 31 \times i}{20} x = \frac{3 - 31 \times i}{20}

Simplify the expression

x = \frac{3}{20} + \frac{31}{20} i x = \frac{3 - 31 \times i}{20}

Simplify the expression

x = \frac{3}{20} + \frac{31}{20} i x = \frac{3}{20} - \frac{31}{20} i

x = 0 x = \frac{3}{20} + \frac{31}{20} i x = \frac{3}{20} - \frac{31}{20} i

Solution

x_{1} = \frac{3}{20} - \frac{31}{20} i, x_{2} = \frac{3}{20} + \frac{31}{20} i, x_{3} = 0

Alternative Form

x_{1} \approx 0.15 - 0.278388 i, x_{2} \approx 0.15 + 0.278388 i, x_{3} = 0

Show Solution