What is 1/2 (1-2)^2-4 ?

The solution to 1/2 (1-2)^2-4 is -7/2

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1/2 (1-2)^2-4

\frac{1}{2} (1 - 2)^{2} - 4

- \frac{7}{2}

Solution steps

\frac{1}{2} (1 - 2)^{2} - 4

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - 2) : - 1

1 - 2

1 - 2 = - 1

= - 1

= \frac{1}{2} (- 1)^{2} - 4

Calculate exponents

(- 1)^{2} : 1

(- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2} = 1

= 1

= \frac{1}{2} \cdot 1 - 4

Multiply and divide (left to right)

\frac{1}{2} \cdot 1 : \frac{1}{2}

\frac{1}{2} \cdot 1

\frac{1}{2} \cdot 1 = \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2} - 4

Add and subtract (left to right)

\frac{1}{2} - 4 : - \frac{7}{2}

\frac{1}{2} - 4

\frac{1}{2} - 4 = - \frac{7}{2}

\frac{1}{2} - 4

Convert element to fraction:

4 = \frac{4 \cdot 2}{2}

= - \frac{4 \cdot 2}{2} + \frac{1}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 4 \cdot 2 + 1}{2}

- 4 \cdot 2 + 1 = - 7

- 4 \cdot 2 + 1

Multiply the numbers:

4 \cdot 2 = 8

= - 8 + 1

Add/Subtract the numbers:

- 8 + 1 = - 7

= - 7

= \frac{- 7}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{7}{2}

= - \frac{7}{2}

= - \frac{7}{2}

(- 3)^{2} + 2 (- 3) + 2

(- 3)^{2} + 2 (- 3) + 3

(- 3)^{2} + 2 (- 3) + 1

324 - 720 + 432

3 \times 5 + 4 \times 2 - 5 \times 4 + 2 \div 2