Pre-Algebra Examples

$- s^{2} = 1 - 2 s$

Step 1

Add $2 s$ to both sides of the equation.

$- s^{2} + 2 s = 1$

Step 2

Subtract $1$ from both sides of the equation.

$- s^{2} + 2 s - 1 = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $- 1$ out of $- s^{2} + 2 s - 1$ .

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Step 3.1.1

Factor $- 1$ out of $- s^{2}$ .

$- (s^{2}) + 2 s - 1 = 0$

Step 3.1.2

Factor $- 1$ out of $2 s$ .

$- (s^{2}) - (- 2 s) - 1 = 0$

Step 3.1.3

Rewrite $- 1$ as $- 1 (1)$ .

$- (s^{2}) - (- 2 s) - 1 \cdot 1 = 0$

Step 3.1.4

Factor $- 1$ out of $- (s^{2}) - (- 2 s)$ .

$- (s^{2} - 2 s) - 1 \cdot 1 = 0$

Step 3.1.5

Factor $- 1$ out of $- (s^{2} - 2 s) - 1 (1)$ .

$- (s^{2} - 2 s + 1) = 0$

Step 3.2

Factor using the perfect square rule.

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Step 3.2.1

Rewrite $1$ as $1^{2}$ .

$- (s^{2} - 2 s + 1^{2}) = 0$

Step 3.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 s = 2 \cdot s \cdot 1$

Step 3.2.3

Rewrite the polynomial.

$- (s^{2} - 2 \cdot s \cdot 1 + 1^{2}) = 0$

Step 3.2.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = s$ and $b = 1$ .

$- {(s - 1)}^{2} = 0$

Step 4

Divide each term in $- {(s - 1)}^{2} = 0$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- {(s - 1)}^{2} = 0$ by $- 1$ .

$\frac{- {(s - 1)}^{2}}{- 1} = \frac{0}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{{(s - 1)}^{2}}{1} = \frac{0}{- 1}$

Step 4.2.2

Divide ${(s - 1)}^{2}$ by $1$ .

${(s - 1)}^{2} = \frac{0}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 1$ .

${(s - 1)}^{2} = 0$

Step 5

Set the $s - 1$ equal to $0$ .

$s - 1 = 0$

Step 6

Add $1$ to both sides of the equation.

$s = 1$