Solve 7w^2-2w-5/21w 15

Question

Simplify the expression

7 w^{2} - \frac{39}{7} w

Evaluate

7 w^{2} - 2 w - \frac{5}{21} w \times 15

Multiply the terms

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Multiply the terms

- \frac{5}{21} w \times 15

Multiply the terms

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Evaluate

\frac{5}{21} \times 15

Reduce the numbers

\frac{5}{7} \times 5

Multiply the numbers

\frac{5 \times 5}{7}

Multiply the numbers

\frac{25}{7}

- \frac{25}{7} w

7 w^{2} - 2 w - \frac{25}{7} w

Solution

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Evaluate

- 2 w - \frac{25}{7} w

Collect like terms by calculating the sum or difference of their coefficients

(- 2 - \frac{25}{7}) w

Subtract the numbers

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Evaluate

- 2 - \frac{25}{7}

Reduce fractions to a common denominator

- \frac{2 \times 7}{7} - \frac{25}{7}

Write all numerators above the common denominator

\frac{- 2 \times 7 - 25}{7}

Multiply the numbers

\frac{- 14 - 25}{7}

Subtract the numbers

\frac{- 39}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{39}{7}

- \frac{39}{7} w

7 w^{2} - \frac{39}{7} w

Show Solution

Factor the expression

\frac{1}{7} w (49 w - 39)

Evaluate

7 w^{2} - 2 w - \frac{5}{21} w \times 15

Multiply the terms

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Multiply the terms

\frac{5}{21} w \times 15

Multiply the terms

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Evaluate

\frac{5}{21} \times 15

Reduce the numbers

\frac{5}{7} \times 5

Multiply the numbers

\frac{5 \times 5}{7}

Multiply the numbers

\frac{25}{7}

\frac{25}{7} w

7 w^{2} - 2 w - \frac{25}{7} w

Subtract the terms

More Steps

Evaluate

- 2 w - \frac{25}{7} w

Collect like terms by calculating the sum or difference of their coefficients

(- 2 - \frac{25}{7}) w

Subtract the numbers

More Steps

Evaluate

- 2 - \frac{25}{7}

Reduce fractions to a common denominator

- \frac{2 \times 7}{7} - \frac{25}{7}

Write all numerators above the common denominator

\frac{- 2 \times 7 - 25}{7}

Multiply the numbers

\frac{- 14 - 25}{7}

Subtract the numbers

\frac{- 39}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{39}{7}

- \frac{39}{7} w

7 w^{2} - \frac{39}{7} w

Rewrite the expression

\frac{1}{7} w \times 49 w - \frac{1}{7} w \times 39

Solution

\frac{1}{7} w (49 w - 39)

Show Solution

Find the roots

w_{1} = 0, w_{2} = \frac{39}{49}

Alternative Form

w_{1} = 0, w_{2} \approx 0.795918

Evaluate

7 w^{2} - 2 w - \frac{5}{21} w \times 15

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

7 w^{2} - 2 w - \frac{5}{21} w \times 15 = 0

Multiply the terms

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Multiply the terms

\frac{5}{21} w \times 15

Multiply the terms

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Evaluate

\frac{5}{21} \times 15

Reduce the numbers

\frac{5}{7} \times 5

Multiply the numbers

\frac{5 \times 5}{7}

Multiply the numbers

\frac{25}{7}

\frac{25}{7} w

7 w^{2} - 2 w - \frac{25}{7} w = 0

Subtract the terms

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Simplify

7 w^{2} - 2 w - \frac{25}{7} w

Subtract the terms

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Evaluate

- 2 w - \frac{25}{7} w

Collect like terms by calculating the sum or difference of their coefficients

(- 2 - \frac{25}{7}) w

Subtract the numbers

- \frac{39}{7} w

7 w^{2} - \frac{39}{7} w

7 w^{2} - \frac{39}{7} w = 0

Factor the expression

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Evaluate

7 w^{2} - \frac{39}{7} w

Rewrite the expression

\frac{1}{7} w \times 49 w - \frac{1}{7} w \times 39

Factor out \frac{1}{7} w from the expression

\frac{1}{7} w (49 w - 39)

\frac{1}{7} w (49 w - 39) = 0

When the product of factors equals 0,at least one factor is 0

\frac{1}{7} w = 0 49 w - 39 = 0

Solve the equation for w

w = 0 49 w - 39 = 0

Solve the equation for w

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Evaluate

49 w - 39 = 0

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

49 w = 0 + 39

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

49 w = 39

Divide both sides

\frac{49 w}{49} = \frac{39}{49}

Divide the numbers

w = \frac{39}{49}

w = 0 w = \frac{39}{49}

Solution

w_{1} = 0, w_{2} = \frac{39}{49}

Alternative Form

w_{1} = 0, w_{2} \approx 0.795918

Show Solution