Algebra Examples

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

Step 1

Subtract $2 {(x - 1)}^{2}$ from both sides of the equation.

$x + 9 - 2 {(x - 1)}^{2} = 0$

Step 2

Simplify $x + 9 - 2 {(x - 1)}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$x + 9 - 2 ((x - 1) (x - 1)) = 0$

Step 2.1.2

Expand $(x - 1) (x - 1)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$x + 9 - 2 (x (x - 1) - 1 (x - 1)) = 0$

Step 2.1.2.2

Apply the distributive property.

$x + 9 - 2 (x \cdot x + x \cdot - 1 - 1 (x - 1)) = 0$

Step 2.1.2.3

Apply the distributive property.

$x + 9 - 2 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) = 0$

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 $x$ .

$x + 9 - 2 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) = 0$

Step 2.1.3.1.2

Move $- 1$ to the left of $x$ .

$x + 9 - 2 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) = 0$

Step 2.1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$x + 9 - 2 (x^{2} - x - 1 x - 1 \cdot - 1) = 0$

Step 2.1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$x + 9 - 2 (x^{2} - x - x - 1 \cdot - 1) = 0$

Step 2.1.3.1.5

Multiply $- 1$ by $- 1$ .

$x + 9 - 2 (x^{2} - x - x + 1) = 0$

Step 2.1.3.2

Subtract $x$ from $- x$ .

$x + 9 - 2 (x^{2} - 2 x + 1) = 0$

Step 2.1.4

Apply the distributive property.

$x + 9 - 2 x^{2} - 2 (- 2 x) - 2 \cdot 1 = 0$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $- 2$ by $- 2$ .

$x + 9 - 2 x^{2} + 4 x - 2 \cdot 1 = 0$

Step 2.1.5.2

Multiply $- 2$ by $1$ .

$x + 9 - 2 x^{2} + 4 x - 2 = 0$

Step 2.2

Add $x$ and $4 x$ .

$5 x + 9 - 2 x^{2} - 2 = 0$

Step 2.3

Subtract $2$ from $9$ .

$5 x - 2 x^{2} + 7 = 0$

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

Reorder $5 x$ and $- 2 x^{2}$ .

$- 2 x^{2} + 5 x + 7 = 0$

Step 5