Write in Standard Form x+3=(2-x)^2

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

Step 1

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

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

Step 2

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

Simplify each term.

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

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

Expand $(2 - x) (2 - x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$x + 3 - (4 + 2 (- x) - x \cdot 2 - x (- x)) = 0$

Multiply $- 1$ by $2$ .

$x + 3 - (4 - 2 x - x \cdot 2 - x (- x)) = 0$

Multiply $2$ by $- 1$ .

$x + 3 - (4 - 2 x - 2 x - x (- x)) = 0$

Rewrite using the commutative property of multiplication.

$x + 3 - (4 - 2 x - 2 x - 1 \cdot - 1 x \cdot x) = 0$

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

Move $x$ .

$x + 3 - (4 - 2 x - 2 x - 1 \cdot - 1 (x \cdot x)) = 0$

Multiply $x$ by $x$ .

$x + 3 - (4 - 2 x - 2 x - 1 \cdot - 1 x^{2}) = 0$

Multiply $- 1$ by $- 1$ .

$x + 3 - (4 - 2 x - 2 x + 1 x^{2}) = 0$

Multiply $x^{2}$ by $1$ .

$x + 3 - (4 - 2 x - 2 x + x^{2}) = 0$

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

$x + 3 - (4 - 4 x + x^{2}) = 0$

Apply the distributive property.

$x + 3 - 1 \cdot 4 - (- 4 x) - x^{2} = 0$

Simplify.

Multiply $- 1$ by $4$ .

$x + 3 - 4 - (- 4 x) - x^{2} = 0$

Multiply $- 4$ by $- 1$ .

$x + 3 - 4 + 4 x - x^{2} = 0$

Add $x$ and $4 x$ .

$5 x + 3 - 4 - x^{2} = 0$

Subtract $4$ from $3$ .

$5 x - 1 - x^{2} = 0$

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

Move $- 1$ .

$5 x - x^{2} - 1 = 0$

Step 5

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

$- x^{2} + 5 x - 1 = 0$

Step 6

Write in Standard Form x+3=(2-x)^2

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