Solve d^3 2d^2-13d 10

Question

Simplify the expression

2 d^{5} - 130 d

Evaluate

d^{3} \times 2 d^{2} - 13 d \times 10

Multiply

More Steps

Multiply the terms

d^{3} \times 2 d^{2}

Multiply the terms with the same base by adding their exponents

d^{3 + 2} \times 2

Add the numbers

d^{5} \times 2

Use the commutative property to reorder the terms

2 d^{5}

2 d^{5} - 13 d \times 10

Solution

2 d^{5} - 130 d

Show Solution

2 d (d^{4} - 65)

Evaluate

d^{3} \times 2 d^{2} - 13 d \times 10

Multiply

More Steps

Multiply the terms

d^{3} \times 2 d^{2}

Multiply the terms with the same base by adding their exponents

d^{3 + 2} \times 2

Add the numbers

d^{5} \times 2

Use the commutative property to reorder the terms

2 d^{5}

2 d^{5} - 13 d \times 10

Multiply the terms

2 d^{5} - 130 d

Rewrite the expression

2 d \times d^{4} - 2 d \times 65

Solution

2 d (d^{4} - 65)

Show Solution

d_{1} = - 465, d_{2} = 0, d_{3} = 465

Alternative Form

d_{1} \approx - 2.839412, d_{2} = 0, d_{3} \approx 2.839412

Evaluate

d^{3} \times 2 d^{2} - 13 d \times 10

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

d^{3} \times 2 d^{2} - 13 d \times 10 = 0

Multiply

More Steps

Multiply the terms

d^{3} \times 2 d^{2}

Multiply the terms with the same base by adding their exponents

d^{3 + 2} \times 2

Add the numbers

d^{5} \times 2

Use the commutative property to reorder the terms

2 d^{5}

2 d^{5} - 13 d \times 10 = 0

Multiply the terms

2 d^{5} - 130 d = 0

Factor the expression

2 d (d^{4} - 65) = 0

Divide both sides

d (d^{4} - 65) = 0

Separate the equation into 2 possible cases

d = 0 d^{4} - 65 = 0

Solve the equation

More Steps

Evaluate

d^{4} - 65 = 0

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

d^{4} = 0 + 65

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

d^{4} = 65

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

d = \pm 465

Separate the equation into 2 possible cases

d = 465 d = - 465

d = 0 d = 465 d = - 465

Solution

d_{1} = - 465, d_{2} = 0, d_{3} = 465

Alternative Form

d_{1} \approx - 2.839412, d_{2} = 0, d_{3} \approx 2.839412

Show Solution