Basic Math Examples

$h^{2} + {(34 - h)}^{2} = 13^{2}$

Step 1

Raise $13$ to the power of $2$ .

$h^{2} + {(34 - h)}^{2} = 169$

Step 2

Move all terms to the left side of the equation and simplify.

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Step 2.1

Subtract $169$ from both sides of the equation.

$h^{2} + {(34 - h)}^{2} - 169 = 0$

Step 2.2

Simplify $h^{2} + {(34 - h)}^{2} - 169$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Rewrite ${(34 - h)}^{2}$ as $(34 - h) (34 - h)$ .

$h^{2} + (34 - h) (34 - h) - 169 = 0$

Step 2.2.1.2

Expand $(34 - h) (34 - h)$ using the FOIL Method.

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Step 2.2.1.2.1

Apply the distributive property.

$h^{2} + 34 (34 - h) - h (34 - h) - 169 = 0$

Step 2.2.1.2.2

Apply the distributive property.

$h^{2} + 34 \cdot 34 + 34 (- h) - h (34 - h) - 169 = 0$

Step 2.2.1.2.3

Apply the distributive property.

$h^{2} + 34 \cdot 34 + 34 (- h) - h \cdot 34 - h (- h) - 169 = 0$

Step 2.2.1.3

Simplify and combine like terms.

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Step 2.2.1.3.1

Simplify each term.

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Step 2.2.1.3.1.1

Multiply $34$ by $34$ .

$h^{2} + 1156 + 34 (- h) - h \cdot 34 - h (- h) - 169 = 0$

Step 2.2.1.3.1.2

Multiply $- 1$ by $34$ .

$h^{2} + 1156 - 34 h - h \cdot 34 - h (- h) - 169 = 0$

Step 2.2.1.3.1.3

Multiply $34$ by $- 1$ .

$h^{2} + 1156 - 34 h - 34 h - h (- h) - 169 = 0$

Step 2.2.1.3.1.4

Rewrite using the commutative property of multiplication.

$h^{2} + 1156 - 34 h - 34 h - 1 \cdot - 1 h \cdot h - 169 = 0$

Step 2.2.1.3.1.5

Multiply $h$ by $h$ by adding the exponents.

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Step 2.2.1.3.1.5.1

Move $h$ .

$h^{2} + 1156 - 34 h - 34 h - 1 \cdot - 1 (h \cdot h) - 169 = 0$

Step 2.2.1.3.1.5.2

Multiply $h$ by $h$ .

$h^{2} + 1156 - 34 h - 34 h - 1 \cdot - 1 h^{2} - 169 = 0$

Step 2.2.1.3.1.6

Multiply $- 1$ by $- 1$ .

$h^{2} + 1156 - 34 h - 34 h + 1 h^{2} - 169 = 0$

Step 2.2.1.3.1.7

Multiply $h^{2}$ by $1$ .

$h^{2} + 1156 - 34 h - 34 h + h^{2} - 169 = 0$

Step 2.2.1.3.2

Subtract $34 h$ from $- 34 h$ .

$h^{2} + 1156 - 68 h + h^{2} - 169 = 0$

Step 2.2.2

Add $h^{2}$ and $h^{2}$ .

$2 h^{2} + 1156 - 68 h - 169 = 0$

Step 2.2.3

Subtract $169$ from $1156$ .

$2 h^{2} - 68 h + 987 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 2$ , $b = - 68$ , and $c = 987$ into the quadratic formula and solve for $h$ .

$\frac{68 \pm \sqrt{{(- 68)}^{2} - 4 \cdot (2 \cdot 987)}}{2 \cdot 2}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $- 68$ to the power of $2$ .

$h = \frac{68 \pm \sqrt{4624 - 4 \cdot 2 \cdot 987}}{2 \cdot 2}$

Step 5.1.2

Multiply $- 4 \cdot 2 \cdot 987$ .

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Step 5.1.2.1

Multiply $- 4$ by $2$ .

$h = \frac{68 \pm \sqrt{4624 - 8 \cdot 987}}{2 \cdot 2}$

Step 5.1.2.2

Multiply $- 8$ by $987$ .

$h = \frac{68 \pm \sqrt{4624 - 7896}}{2 \cdot 2}$

Step 5.1.3

Subtract $7896$ from $4624$ .

$h = \frac{68 \pm \sqrt{- 3272}}{2 \cdot 2}$

Step 5.1.4

Rewrite $- 3272$ as $- 1 (3272)$ .

$h = \frac{68 \pm \sqrt{- 1 \cdot 3272}}{2 \cdot 2}$

Step 5.1.5

Rewrite $\sqrt{- 1 (3272)}$ as $\sqrt{- 1} \cdot \sqrt{3272}$ .

$h = \frac{68 \pm \sqrt{- 1} \cdot \sqrt{3272}}{2 \cdot 2}$

Step 5.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$h = \frac{68 \pm i \cdot \sqrt{3272}}{2 \cdot 2}$

Step 5.1.7

Rewrite $3272$ as $2^{2} \cdot 818$ .

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Step 5.1.7.1

Factor $4$ out of $3272$ .

$h = \frac{68 \pm i \cdot \sqrt{4 (818)}}{2 \cdot 2}$

Step 5.1.7.2

Rewrite $4$ as $2^{2}$ .

$h = \frac{68 \pm i \cdot \sqrt{2^{2} \cdot 818}}{2 \cdot 2}$

Step 5.1.8

Pull terms out from under the radical.

$h = \frac{68 \pm i \cdot (2 \sqrt{818})}{2 \cdot 2}$

Step 5.1.9

Move $2$ to the left of $i$ .

$h = \frac{68 \pm 2 i \sqrt{818}}{2 \cdot 2}$

Step 5.2

Multiply $2$ by $2$ .

$h = \frac{68 \pm 2 i \sqrt{818}}{4}$

Step 5.3

Simplify $\frac{68 \pm 2 i \sqrt{818}}{4}$ .

$h = \frac{34 \pm i \sqrt{818}}{2}$

Step 6

The final answer is the combination of both solutions.

$h = \frac{34 + i \sqrt{818}}{2}, \frac{34 - i \sqrt{818}}{2}$