Solve 1/10(x-4)(x-5)

Question

Simplify the expression

\frac{1}{10} x^{2} - \frac{9}{10} x + 2

Evaluate

\frac{1}{10} (x - 4) (x - 5)

Multiply the first two terms

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Evaluate

\frac{1}{10} (x - 4)

Apply the distributive property

\frac{1}{10} x - \frac{1}{10} \times 4

Multiply the numbers

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Evaluate

\frac{1}{10} \times 4

Reduce the numbers

\frac{1}{5} \times 2

Multiply the numbers

\frac{2}{5}

\frac{1}{10} x - \frac{2}{5}

(\frac{1}{10} x - \frac{2}{5}) (x - 5)

Apply the distributive property

\frac{1}{10} x \times x - \frac{1}{10} x \times 5 - \frac{2}{5} x - (- \frac{2}{5} \times 5)

Multiply the terms

\frac{1}{10} x^{2} - \frac{1}{10} x \times 5 - \frac{2}{5} x - (- \frac{2}{5} \times 5)

Multiply the numbers

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Evaluate

\frac{1}{10} \times 5

Reduce the numbers

\frac{1}{2} \times 1

Multiply the numbers

\frac{1}{2}

\frac{1}{10} x^{2} - \frac{1}{2} x - \frac{2}{5} x - (- \frac{2}{5} \times 5)

Multiply the numbers

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Evaluate

- \frac{2}{5} \times 5

Reduce the numbers

- 2 \times 1

Simplify

- 2

\frac{1}{10} x^{2} - \frac{1}{2} x - \frac{2}{5} x - (- 2)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

\frac{1}{10} x^{2} - \frac{1}{2} x - \frac{2}{5} x + 2

Solution

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Evaluate

- \frac{1}{2} x - \frac{2}{5} x

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

(- \frac{1}{2} - \frac{2}{5}) x

Subtract the numbers

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Evaluate

- \frac{1}{2} - \frac{2}{5}

Reduce fractions to a common denominator

- \frac{5}{2 \times 5} - \frac{2 \times 2}{5 \times 2}

Multiply the numbers

- \frac{5}{10} - \frac{2 \times 2}{5 \times 2}

Multiply the numbers

- \frac{5}{10} - \frac{2 \times 2}{10}

Write all numerators above the common denominator

\frac{- 5 - 2 \times 2}{10}

Multiply the numbers

\frac{- 5 - 4}{10}

Subtract the numbers

\frac{- 9}{10}

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

- \frac{9}{10}

- \frac{9}{10} x

\frac{1}{10} x^{2} - \frac{9}{10} x + 2

Show Solution

Find the roots

x_{1} = 4, x_{2} = 5

Evaluate

\frac{1}{10} (x - 4) (x - 5)

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

\frac{1}{10} (x - 4) (x - 5) = 0

Multiply the first two terms

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Multiply the terms

\frac{1}{10} (x - 4) (x - 5)

Multiply the first two terms

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Evaluate

\frac{1}{10} (x - 4)

Apply the distributive property

\frac{1}{10} x - \frac{1}{10} \times 4

Multiply the numbers

\frac{1}{10} x - \frac{2}{5}

(\frac{1}{10} x - \frac{2}{5}) (x - 5)

(\frac{1}{10} x - \frac{2}{5}) (x - 5) = 0

Separate the equation into 2 possible cases

\frac{1}{10} x - \frac{2}{5} = 0 x - 5 = 0

Solve the equation

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Evaluate

\frac{1}{10} x - \frac{2}{5} = 0

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

\frac{1}{10} x = 0 + \frac{2}{5}

Add the terms

\frac{1}{10} x = \frac{2}{5}

Multiply by the reciprocal

\frac{1}{10} x \times 10 = \frac{2}{5} \times 10

Multiply

x = \frac{2}{5} \times 10

Multiply

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Evaluate

\frac{2}{5} \times 10

Reduce the numbers

2 \times 2

Multiply the numbers

4

x = 4

x = 4 x - 5 = 0

Solve the equation

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Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 4 x = 5

Solution

x_{1} = 4, x_{2} = 5

Show Solution