Algebra Examples

${(x - 3)}^{2} - 2 x = 9$

Step 1

Subtract $9$ from both sides of the equation.

${(x - 3)}^{2} - 2 x - 9 = 0$

Step 2

Simplify ${(x - 3)}^{2} - 2 x - 9$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$(x - 3) (x - 3) - 2 x - 9 = 0$

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

$x (x - 3) - 3 (x - 3) - 2 x - 9 = 0$

Step 2.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) - 2 x - 9 = 0$

Step 2.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 - 2 x - 9 = 0$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 - 2 x - 9 = 0$

Step 2.1.3.1.2

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

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 - 2 x - 9 = 0$

Step 2.1.3.1.3

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 - 2 x - 9 = 0$

Step 2.1.3.2

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

$x^{2} - 6 x + 9 - 2 x - 9 = 0$

Step 2.2

Combine the opposite terms in $x^{2} - 6 x + 9 - 2 x - 9$ .

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Step 2.2.1

Subtract $9$ from $9$ .

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

Step 2.2.2

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

$x^{2} - 6 x - 2 x = 0$

Step 2.3

Subtract $2 x$ from $- 6 x$ .

$x^{2} - 8 x = 0$

Step 3

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 4

The standard form is $x^{2} - 8 x$ .

$x^{2} - 8 x = 0$

Step 5