Trigonometry Examples

${(x - 3)}^{2} + {(4 - 5)}^{2} = 226$

Step 1

Simplify ${(x - 3)}^{2} + {(4 - 5)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$(x - 3) (x - 3) + {(4 - 5)}^{2} = 226$

Step 1.1.2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$x (x - 3) - 3 (x - 3) + {(4 - 5)}^{2} = 226$

Step 1.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) + {(4 - 5)}^{2} = 226$

Step 1.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(4 - 5)}^{2} = 226$

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 $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(4 - 5)}^{2} = 226$

Step 1.1.3.1.2

Move $- 3$ to the left of $x$ .

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 + {(4 - 5)}^{2} = 226$

Step 1.1.3.1.3

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 + {(4 - 5)}^{2} = 226$

Step 1.1.3.2

Subtract $3 x$ from $- 3 x$ .

$x^{2} - 6 x + 9 + {(4 - 5)}^{2} = 226$

Step 1.1.4

Subtract $5$ from $4$ .

$x^{2} - 6 x + 9 + {(- 1)}^{2} = 226$

Step 1.1.5

Raise $- 1$ to the power of $2$ .

$x^{2} - 6 x + 9 + 1 = 226$

Step 1.2

Add $9$ and $1$ .

$x^{2} - 6 x + 10 = 226$

Step 2

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

$x \approx - 12, 18$

Step 3