Trigonometry Examples

${(x + 8)}^{2} + {(x - 8)}^{2} = 104$

Step 1

Simplify ${(x + 8)}^{2} + {(x - 8)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x + 8)}^{2}$ as $(x + 8) (x + 8)$ .

$(x + 8) (x + 8) + {(x - 8)}^{2} = 104$

Step 1.1.2

Expand $(x + 8) (x + 8)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$x (x + 8) + 8 (x + 8) + {(x - 8)}^{2} = 104$

Step 1.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 8 + 8 (x + 8) + {(x - 8)}^{2} = 104$

Step 1.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 8 + 8 x + 8 \cdot 8 + {(x - 8)}^{2} = 104$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 + 8 x + 8 \cdot 8 + {(x - 8)}^{2} = 104$

Step 1.1.3.1.2

Move $8$ to the left of $x$ .

$x^{2} + 8 \cdot x + 8 x + 8 \cdot 8 + {(x - 8)}^{2} = 104$

Step 1.1.3.1.3

Multiply $8$ by $8$ .

$x^{2} + 8 x + 8 x + 64 + {(x - 8)}^{2} = 104$

Step 1.1.3.2

Add $8 x$ and $8 x$ .

$x^{2} + 16 x + 64 + {(x - 8)}^{2} = 104$

Step 1.1.4

Rewrite ${(x - 8)}^{2}$ as $(x - 8) (x - 8)$ .

$x^{2} + 16 x + 64 + (x - 8) (x - 8) = 104$

Step 1.1.5

Expand $(x - 8) (x - 8)$ using the FOIL Method.

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Step 1.1.5.1

Apply the distributive property.

$x^{2} + 16 x + 64 + x (x - 8) - 8 (x - 8) = 104$

Step 1.1.5.2

Apply the distributive property.

$x^{2} + 16 x + 64 + x \cdot x + x \cdot - 8 - 8 (x - 8) = 104$

Step 1.1.5.3

Apply the distributive property.

$x^{2} + 16 x + 64 + x \cdot x + x \cdot - 8 - 8 x - 8 \cdot - 8 = 104$

Step 1.1.6

Simplify and combine like terms.

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Step 1.1.6.1

Simplify each term.

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Step 1.1.6.1.1

Multiply $x$ by $x$ .

$x^{2} + 16 x + 64 + x^{2} + x \cdot - 8 - 8 x - 8 \cdot - 8 = 104$

Step 1.1.6.1.2

Move $- 8$ to the left of $x$ .

$x^{2} + 16 x + 64 + x^{2} - 8 \cdot x - 8 x - 8 \cdot - 8 = 104$

Step 1.1.6.1.3

Multiply $- 8$ by $- 8$ .

$x^{2} + 16 x + 64 + x^{2} - 8 x - 8 x + 64 = 104$

Step 1.1.6.2

Subtract $8 x$ from $- 8 x$ .

$x^{2} + 16 x + 64 + x^{2} - 16 x + 64 = 104$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $x^{2} + 16 x + 64 + x^{2} - 16 x + 64$ .

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Step 1.2.1.1

Subtract $16 x$ from $16 x$ .

$x^{2} + 64 + x^{2} + 0 + 64 = 104$

Step 1.2.1.2

Add $x^{2} + 64 + x^{2}$ and $0$ .

$x^{2} + 64 + x^{2} + 64 = 104$

Step 1.2.2

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

$2 x^{2} + 64 + 64 = 104$

Step 1.2.3

Add $64$ and $64$ .

$2 x^{2} + 128 = 104$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 3