Solve 4j^2120j - 164 = 0

Question

Solve the equation

j = \frac{3 9225}{30}

Alternative Form

j \approx 0.699092

Evaluate

4 j^{2} \times 120 j - 164 = 0

Multiply

More Steps

Evaluate

4 j^{2} \times 120 j

Multiply the terms

480 j^{2} \times j

Multiply the terms with the same base by adding their exponents

480 j^{2 + 1}

Add the numbers

480 j^{3}

480 j^{3} - 164 = 0

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

480 j^{3} = 0 + 164

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

480 j^{3} = 164

Divide both sides

\frac{480 j ^{3}}{480} = \frac{164}{480}

Divide the numbers

j^{3} = \frac{164}{480}

Cancel out the common factor 4

j^{3} = \frac{41}{120}

Take the 3 -th root on both sides of the equation

3 j^{3} = 3 \frac{41}{120}

Calculate

j = 3 \frac{41}{120}

Solution

More Steps

Evaluate

3 \frac{41}{120}

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

\frac{3 41}{3 120}

Simplify the radical expression

More Steps

Evaluate

3120

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 15

Write the number in exponential form with the base of 2

3 2^{3} \times 15

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 315

Reduce the index of the radical and exponent with 3

2315

\frac{3 41}{2 3 15}

Multiply by the Conjugate

\frac{3 41 \times 3 1 5 ^{2}}{2 3 15 \times 3 1 5 ^{2}}

Simplify

\frac{3 41 \times 3 225}{2 3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

341 \times 3225

The product of roots with the same index is equal to the root of the product

3 41 \times 225

Calculate the product

39225

\frac{3 9225}{2 3 15 \times 3 1 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

2315 \times 3 1 5^{2}

Multiply the terms

2 \times 15

Multiply the terms

30

\frac{3 9225}{30}

j = \frac{3 9225}{30}

Alternative Form

j \approx 0.699092

Show Solution