Solve for x (x-6)^2-x(x+8)=2

${(x - 6)}^{2} - x (x + 8) = 2$

Step 1

Simplify each term.

Apply the distributive property.

${(x - 6)}^{2} - x \cdot x - x \cdot 8 = 2$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

${(x - 6)}^{2} - (x \cdot x) - x \cdot 8 = 2$

Multiply $x$ by $x$ .

${(x - 6)}^{2} - x^{2} - x \cdot 8 = 2$

Multiply $8$ by $- 1$ .

${(x - 6)}^{2} - x^{2} - 8 x = 2$

Step 2

Subtract $2$ from both sides of the equation.

${(x - 6)}^{2} - x^{2} - 8 x - 2 = 0$

Step 3

Simplify ${(x - 6)}^{2} - x^{2} - 8 x - 2$ .

Simplify each term.

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

$(x - 6) (x - 6) - x^{2} - 8 x - 2 = 0$

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

Apply the distributive property.

$x (x - 6) - 6 (x - 6) - x^{2} - 8 x - 2 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 (x - 6) - x^{2} - 8 x - 2 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6 - x^{2} - 8 x - 2 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6 - x^{2} - 8 x - 2 = 0$

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

$x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6 - x^{2} - 8 x - 2 = 0$

Multiply $- 6$ by $- 6$ .

$x^{2} - 6 x - 6 x + 36 - x^{2} - 8 x - 2 = 0$

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

$x^{2} - 12 x + 36 - x^{2} - 8 x - 2 = 0$

Combine the opposite terms in $x^{2} - 12 x + 36 - x^{2} - 8 x - 2$ .

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

$- 12 x + 36 + 0 - 8 x - 2 = 0$

Add $- 12 x + 36$ and $0$ .

$- 12 x + 36 - 8 x - 2 = 0$

Subtract $8 x$ from $- 12 x$ .

$- 20 x + 36 - 2 = 0$

Subtract $2$ from $36$ .

$- 20 x + 34 = 0$

Step 4

Factor $- 2$ out of $- 20 x + 34$ .

Factor $- 2$ out of $- 20 x$ .

$- 2 (10 x) + 34 = 0$

Factor $- 2$ out of $34$ .

$- 2 (10 x) - 2 \cdot - 17 = 0$

Factor $- 2$ out of $- 2 (10 x) - 2 (- 17)$ .

$- 2 (10 x - 17) = 0$

Step 5

Divide each term in $- 2 (10 x - 17) = 0$ by $- 2$ and simplify.

Divide each term in $- 2 (10 x - 17) = 0$ by $- 2$ .

$\frac{- 2 (10 x - 17)}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 (10 x - 17)}{- 2} = \frac{0}{- 2}$

Divide $10 x - 17$ by $1$ .

$10 x - 17 = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$10 x - 17 = 0$

Step 6

Add $17$ to both sides of the equation.

$10 x = 17$

Step 7

Divide each term in $10 x = 17$ by $10$ and simplify.

Divide each term in $10 x = 17$ by $10$ .

$\frac{10 x}{10} = \frac{17}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{17}{10}$

Divide $x$ by $1$ .

$x = \frac{17}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{17}{10}$

Decimal Form:

$x = 1.7$

Mixed Number Form:

$x = 1 \frac{7}{10}$

Solve for x (x-6)^2-x(x+8)=2

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