Solve 2m 1/2m-1 - 2m-1/2m 1

Question

Simplify the expression

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

Evaluate

2 m \times \frac{1}{2} m - 1 - 2 m - \frac{1}{2} m \times 1

Multiply

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Multiply the terms

2 m \times \frac{1}{2} m

Multiply the terms

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Evaluate

2 \times \frac{1}{2}

Reduce the fraction

1 \times 1

Any expression multiplied by 1 remains the same

1

m \times m

Multiply the terms

m^{2}

m^{2} - 1 - 2 m - \frac{1}{2} m \times 1

Multiply the terms

m^{2} - 1 - 2 m - \frac{1}{2} m

Solution

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Evaluate

- 2 m - \frac{1}{2} m

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

(- 2 - \frac{1}{2}) m

Subtract the numbers

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Evaluate

- 2 - \frac{1}{2}

Reduce fractions to a common denominator

- \frac{2 \times 2}{2} - \frac{1}{2}

Write all numerators above the common denominator

\frac{- 2 \times 2 - 1}{2}

Multiply the numbers

\frac{- 4 - 1}{2}

Subtract the numbers

\frac{- 5}{2}

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

- \frac{5}{2}

- \frac{5}{2} m

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

Show Solution

Factor the expression

\frac{1}{2} (2 m^{2} - 2 - 5 m)

Evaluate

2 m \times \frac{1}{2} m - 1 - 2 m - \frac{1}{2} m \times 1

Multiply

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Multiply the terms

2 m \times \frac{1}{2} m

Multiply the terms

More Steps

Evaluate

2 \times \frac{1}{2}

Reduce the fraction

1 \times 1

Any expression multiplied by 1 remains the same

1

m \times m

Multiply the terms

m^{2}

m^{2} - 1 - 2 m - \frac{1}{2} m \times 1

Multiply the terms

m^{2} - 1 - 2 m - \frac{1}{2} m

Subtract the terms

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Evaluate

- 2 m - \frac{1}{2} m

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

(- 2 - \frac{1}{2}) m

Subtract the numbers

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Evaluate

- 2 - \frac{1}{2}

Reduce fractions to a common denominator

- \frac{2 \times 2}{2} - \frac{1}{2}

Write all numerators above the common denominator

\frac{- 2 \times 2 - 1}{2}

Multiply the numbers

\frac{- 4 - 1}{2}

Subtract the numbers

\frac{- 5}{2}

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

- \frac{5}{2}

- \frac{5}{2} m

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

Solution

\frac{1}{2} (2 m^{2} - 2 - 5 m)

Show Solution

Find the roots

m_{1} = \frac{5 - 41}{4}, m_{2} = \frac{5 + 41}{4}

Alternative Form

m_{1} \approx - 0.350781, m_{2} \approx 2.850781

Evaluate

2 m \times \frac{1}{2} m - 1 - 2 m - \frac{1}{2} m \times 1

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

2 m \times \frac{1}{2} m - 1 - 2 m - \frac{1}{2} m \times 1 = 0

Multiply

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Multiply the terms

2 m \times \frac{1}{2} m

Multiply the terms

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Evaluate

2 \times \frac{1}{2}

Reduce the fraction

1 \times 1

Any expression multiplied by 1 remains the same

1

m \times m

Multiply the terms

m^{2}

m^{2} - 1 - 2 m - \frac{1}{2} m \times 1 = 0

Multiply the terms

m^{2} - 1 - 2 m - \frac{1}{2} m = 0

Subtract the terms

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Simplify

m^{2} - 1 - 2 m - \frac{1}{2} m

Subtract the terms

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Evaluate

- 2 m - \frac{1}{2} m

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

(- 2 - \frac{1}{2}) m

Subtract the numbers

- \frac{5}{2} m

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

m^{2} - 1 - \frac{5}{2} m = 0

Rewrite in standard form

m^{2} - \frac{5}{2} m - 1 = 0

Multiply both sides

2 (m^{2} - \frac{5}{2} m - 1) = 2 \times 0

Calculate

2 m^{2} - 5 m - 2 = 0

Substitute a= 2,b= - 5 and c= - 2 into the quadratic formula m = \frac{- b \pm b ^{2} - 4 a c}{2 a}

m = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 2 ( - 2 )}{2 \times 2}

Simplify the expression

m = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 2 ( - 2 )}{4}

Simplify the expression

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Evaluate

(- 5)^{2} - 4 \times 2 (- 2)

Multiply

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Multiply the terms

4 \times 2 (- 2)

Rewrite the expression

- 4 \times 2 \times 2

Multiply the terms

- 16

(- 5)^{2} - (- 16)

Rewrite the expression

5^{2} - (- 16)

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

5^{2} + 16

Evaluate the power

25 + 16

Add the numbers

41

m = \frac{5 \pm 41}{4}

Separate the equation into 2 possible cases

m = \frac{5 + 41}{4} m = \frac{5 - 41}{4}

Solution

m_{1} = \frac{5 - 41}{4}, m_{2} = \frac{5 + 41}{4}

Alternative Form

m_{1} \approx - 0.350781, m_{2} \approx 2.850781

Show Solution