Basic Math Examples

$10 H - 0.5 H^{2} = 0.5 H^{2}$

Step 1

Move all terms containing $H$ to the left side of the equation.

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Step 1.1

Subtract $0.5 H^{2}$ from both sides of the equation.

$10 H - 0.5 H^{2} - 0.5 H^{2} = 0$

Step 1.2

Subtract $0.5 H^{2}$ from $- 0.5 H^{2}$ .

$10 H - 1 H^{2} = 0$

Step 2

Factor the left side of the equation.

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Step 2.1

Let $u = H$ . Substitute $u$ for all occurrences of $H$ .

$10 u - 1 u^{2} = 0$

Step 2.2

Factor $u$ out of $10 u - 1 u^{2}$ .

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Step 2.2.1

Factor $u$ out of $10 u$ .

$u \cdot 10 - 1 u^{2} = 0$

Step 2.2.2

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

$u \cdot 10 + u (- 1 u) = 0$

Step 2.2.3

Factor $u$ out of $u \cdot 10 + u (- 1 u)$ .

$u (10 - 1 u) = 0$

Step 2.3

Factor.

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Step 2.3.1

Factor $1$ out of $10 - 1 u$ .

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Step 2.3.1.1

Rewrite $10$ as $1 (10)$ .

$u (1 (10) - 1 u) = 0$

Step 2.3.1.2

Factor $1$ out of $- 1 u$ .

$u (1 (10) + 1 (- u)) = 0$

Step 2.3.1.3

Factor $1$ out of $1 (10) + 1 (- u)$ .

$u (1 (10 - u)) = 0$

Step 2.3.2

Remove unnecessary parentheses.

$u \cdot (1 (10 - u)) = 0$

Step 2.4

Multiply $u$ by $1$ .

$u (10 - u) = 0$

Step 2.5

Replace all occurrences of $u$ with $H$ .

$H (10 - H) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$H = 0$

$10 - H = 0$

Step 4

Set $H$ equal to $0$ .

$H = 0$

Step 5

Set $10 - H$ equal to $0$ and solve for $H$ .

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Step 5.1

Set $10 - H$ equal to $0$ .

$10 - H = 0$

Step 5.2

Solve $10 - H = 0$ for $H$ .

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Step 5.2.1

Subtract $10$ from both sides of the equation.

$- H = - 10$

Step 5.2.2

Divide each term in $- H = - 10$ by $- 1$ and simplify.

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Step 5.2.2.1

Divide each term in $- H = - 10$ by $- 1$ .

$\frac{- H}{- 1} = \frac{- 10}{- 1}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{H}{1} = \frac{- 10}{- 1}$

Step 5.2.2.2.2

Divide $H$ by $1$ .

$H = \frac{- 10}{- 1}$

Step 5.2.2.3

Simplify the right side.

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Step 5.2.2.3.1

Divide $- 10$ by $- 1$ .

$H = 10$

Step 6

The final solution is all the values that make $H (10 - H) = 0$ true.

$H = 0, 10$