Solve 2(2j^3) - 3j

Question

Simplify the expression

4 j^{3} - 3 j

Evaluate

2 \times 2 j^{3} - 3 j

Solution

4 j^{3} - 3 j

Show Solution

j (4 j^{2} - 3)

Evaluate

2 \times 2 j^{3} - 3 j

Multiply the numbers

More Steps

Evaluate

2 \times 2

Multiply the numbers

4

Evaluate

4 j^{3}

4 j^{3} - 3 j

Rewrite the expression

j \times 4 j^{2} - j \times 3

Solution

j (4 j^{2} - 3)

Show Solution

j_{1} = - \frac{3}{2}, j_{2} = 0, j_{3} = \frac{3}{2}

Alternative Form

j_{1} \approx - 0.866025, j_{2} = 0, j_{3} \approx 0.866025

Evaluate

2 (2 j^{3}) - 3 j

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

2 (2 j^{3}) - 3 j = 0

Multiply the terms

2 \times 2 j^{3} - 3 j = 0

Multiply the numbers

4 j^{3} - 3 j = 0

Factor the expression

j (4 j^{2} - 3) = 0

Separate the equation into 2 possible cases

j = 0 4 j^{2} - 3 = 0

Solve the equation

More Steps

Evaluate

4 j^{2} - 3 = 0

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

4 j^{2} = 0 + 3

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

4 j^{2} = 3

Divide both sides

\frac{4 j ^{2}}{4} = \frac{3}{4}

Divide the numbers

j^{2} = \frac{3}{4}

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

j = \pm \frac{3}{4}

Simplify the expression

More Steps

Evaluate

\frac{3}{4}

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

\frac{3}{4}

Simplify the radical expression

\frac{3}{2}

j = \pm \frac{3}{2}

Separate the equation into 2 possible cases

j = \frac{3}{2} j = - \frac{3}{2}

j = 0 j = \frac{3}{2} j = - \frac{3}{2}

Solution

j_{1} = - \frac{3}{2}, j_{2} = 0, j_{3} = \frac{3}{2}

Alternative Form

j_{1} \approx - 0.866025, j_{2} = 0, j_{3} \approx 0.866025

Show Solution