Solve 10:j^2-j14 - ScanMath

Question

Simplify the expression

\frac{10 - 14 j ^{3}}{j ^{2}}

Evaluate

10 \div j^{2} - j \times 14

Rewrite the expression

\frac{10}{j ^{2}} - j \times 14

Use the commutative property to reorder the terms

\frac{10}{j ^{2}} - 14 j

Reduce fractions to a common denominator

\frac{10}{j ^{2}} - \frac{14 j \times j ^{2}}{j ^{2}}

Write all numerators above the common denominator

\frac{10 - 14 j \times j ^{2}}{j ^{2}}

Solution

More Steps

Evaluate

j \times j^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

j^{1 + 2}

Add the numbers

j^{3}

\frac{10 - 14 j ^{3}}{j ^{2}}

Show Solution

Find the excluded values

j = 0

Evaluate

10 \div j^{2} - j \times 14

To find the excluded values,set the denominators equal to 0

j^{2} = 0

Solution

j = 0

Show Solution

Find the roots

j = \frac{3 245}{7}

Alternative Form

j \approx 0.893904

Evaluate

10 \div j^{2} - j \times 14

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

10 \div j^{2} - j \times 14 = 0

The only way a power can not be 0 is when the base not equals 0

10 \div j^{2} - j \times 14 = 0, j \neq = 0

Calculate

10 \div j^{2} - j \times 14 = 0

Rewrite the expression

\frac{10}{j ^{2}} - j \times 14 = 0

Use the commutative property to reorder the terms

\frac{10}{j ^{2}} - 14 j = 0

Subtract the terms

More Steps

Simplify

\frac{10}{j ^{2}} - 14 j

Reduce fractions to a common denominator

\frac{10}{j ^{2}} - \frac{14 j \times j ^{2}}{j ^{2}}

Write all numerators above the common denominator

\frac{10 - 14 j \times j ^{2}}{j ^{2}}

Multiply the terms

More Steps

Evaluate

j \times j^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

j^{1 + 2}

Add the numbers

j^{3}

\frac{10 - 14 j ^{3}}{j ^{2}}

\frac{10 - 14 j ^{3}}{j ^{2}} = 0

Cross multiply

10 - 14 j^{3} = j^{2} \times 0

Simplify the equation

10 - 14 j^{3} = 0

Rewrite the expression

- 14 j^{3} = - 10

Change the signs on both sides of the equation

14 j^{3} = 10

Divide both sides

\frac{14 j ^{3}}{14} = \frac{10}{14}

Divide the numbers

j^{3} = \frac{10}{14}

Cancel out the common factor 2

j^{3} = \frac{5}{7}

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

3 j^{3} = 3 \frac{5}{7}

Calculate

j = 3 \frac{5}{7}

Simplify the root

More Steps

Evaluate

3 \frac{5}{7}

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

\frac{3 5}{3 7}

Multiply by the Conjugate

\frac{3 5 \times 3 7 ^{2}}{3 7 \times 3 7 ^{2}}

Simplify

\frac{3 5 \times 3 49}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

35 \times 349

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

3 5 \times 49

Calculate the product

3245

\frac{3 245}{3 7 \times 3 7 ^{2}}

Multiply the numbers

More Steps

Evaluate

37 \times 3 7^{2}

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

3 7 \times 7^{2}

Calculate the product

3 7^{3}

Reduce the index of the radical and exponent with 3

7

\frac{3 245}{7}

j = \frac{3 245}{7}

Check if the solution is in the defined range

j = \frac{3 245}{7}, j \neq = 0

Solution

j = \frac{3 245}{7}

Alternative Form

j \approx 0.893904

Show Solution