Examples

${(x + 5)}^{2} - y^{2} = 125$

Step 1

Simplify the left side ${(x + 5)}^{2} - y^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x + 5)}^{2}$ as $(x + 5) (x + 5)$ .

$(x + 5) (x + 5) - y^{2} = 125$

Step 1.1.2

Expand $(x + 5) (x + 5)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$x (x + 5) + 5 (x + 5) - y^{2} = 125$

Step 1.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 5 + 5 (x + 5) - y^{2} = 125$

Step 1.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5 - y^{2} = 125$

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 $x$ .

$x^{2} + x \cdot 5 + 5 x + 5 \cdot 5 - y^{2} = 125$

Step 1.1.3.1.2

Move $5$ to the left of $x$ .

$x^{2} + 5 \cdot x + 5 x + 5 \cdot 5 - y^{2} = 125$

Step 1.1.3.1.3

Multiply $5$ by $5$ .

$x^{2} + 5 x + 5 x + 25 - y^{2} = 125$

Step 1.1.3.2

Add $5 x$ and $5 x$ .

$x^{2} + 10 x + 25 - y^{2} = 125$

Step 1.2

Reorder.

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Step 1.2.1

Move $25$ .

$x^{2} + 10 x - y^{2} + 25 = 125$

Step 1.2.2

Move $10 x$ .

$x^{2} - y^{2} + 10 x + 25 = 125$

Step 2

Set the equation equal to zero.

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Step 2.1

Subtract $125$ from both sides of the equation.

$x^{2} - y^{2} + 10 x + 25 - 125 = 0$

Step 2.2

Subtract $125$ from $25$ .

$x^{2} - y^{2} + 10 x - 100 = 0$

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