Algebra Examples

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

Step 1

Simplify ${(x + 6)}^{2}$ .

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Step 1.1

Rewrite ${(x + 6)}^{2}$ as $(x + 6) (x + 6)$ .

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

Step 1.2

Expand $(x + 6) (x + 6)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Apply the distributive property.

${(x - 6)}^{2} + x^{2} = x \cdot x + x \cdot 6 + 6 (x + 6)$

Step 1.2.3

Apply the distributive property.

${(x - 6)}^{2} + x^{2} = x \cdot x + x \cdot 6 + 6 x + 6 \cdot 6$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

${(x - 6)}^{2} + x^{2} = x^{2} + x \cdot 6 + 6 x + 6 \cdot 6$

Step 1.3.1.2

Move $6$ to the left of $x$ .

${(x - 6)}^{2} + x^{2} = x^{2} + 6 \cdot x + 6 x + 6 \cdot 6$

Step 1.3.1.3

Multiply $6$ by $6$ .

${(x - 6)}^{2} + x^{2} = x^{2} + 6 x + 6 x + 36$

Step 1.3.2

Add $6 x$ and $6 x$ .

${(x - 6)}^{2} + x^{2} = x^{2} + 12 x + 36$

Step 2

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

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Step 2.1

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

${(x - 6)}^{2} + x^{2} - x^{2} = 12 x + 36$

Step 2.2

Subtract $12 x$ from both sides of the equation.

${(x - 6)}^{2} + x^{2} - x^{2} - 12 x = 36$

Step 2.3

Combine the opposite terms in ${(x - 6)}^{2} + x^{2} - x^{2} - 12 x$ .

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Step 2.3.1

Subtract $x^{2}$ from $x^{2}$ .

${(x - 6)}^{2} + 0 - 12 x = 36$

Step 2.3.2

Add ${(x - 6)}^{2}$ and $0$ .

${(x - 6)}^{2} - 12 x = 36$

Step 2.4

Simplify each term.

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Step 2.4.1

Rewrite ${(x - 6)}^{2}$ as $(x - 6) (x - 6)$ .

$(x - 6) (x - 6) - 12 x = 36$

Step 2.4.2

Expand $(x - 6) (x - 6)$ using the FOIL Method.

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Step 2.4.2.1

Apply the distributive property.

$x (x - 6) - 6 (x - 6) - 12 x = 36$

Step 2.4.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 (x - 6) - 12 x = 36$

Step 2.4.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6 - 12 x = 36$

Step 2.4.3

Simplify and combine like terms.

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Step 2.4.3.1

Simplify each term.

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Step 2.4.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6 - 12 x = 36$

Step 2.4.3.1.2

Move $- 6$ to the left of $x$ .

$x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6 - 12 x = 36$

Step 2.4.3.1.3

Multiply $- 6$ by $- 6$ .

$x^{2} - 6 x - 6 x + 36 - 12 x = 36$

Step 2.4.3.2

Subtract $6 x$ from $- 6 x$ .

$x^{2} - 12 x + 36 - 12 x = 36$

Step 2.5

Subtract $12 x$ from $- 12 x$ .

$x^{2} - 24 x + 36 = 36$

Step 3

Subtract $36$ from both sides of the equation.

$x^{2} - 24 x + 36 - 36 = 0$

Step 4

Combine the opposite terms in $x^{2} - 24 x + 36 - 36$ .

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Step 4.1

Subtract $36$ from $36$ .

$x^{2} - 24 x + 0 = 0$

Step 4.2

Add $x^{2} - 24 x$ and $0$ .

$x^{2} - 24 x = 0$

Step 5

Factor $x$ out of $x^{2} - 24 x$ .

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Step 5.1

Factor $x$ out of $x^{2}$ .

$x \cdot x - 24 x = 0$

Step 5.2

Factor $x$ out of $- 24 x$ .

$x \cdot x + x \cdot - 24 = 0$

Step 5.3

Factor $x$ out of $x \cdot x + x \cdot - 24$ .

$x (x - 24) = 0$

Step 6

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

$x = 0$

$x - 24 = 0$

Step 7

Set $x$ equal to $0$ .

$x = 0$

Step 8

Set $x - 24$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x - 24$ equal to $0$ .

$x - 24 = 0$

Step 8.2

Add $24$ to both sides of the equation.

$x = 24$

Step 9

The final solution is all the values that make $x (x - 24) = 0$ true.

$x = 0, 24$