Write in Standard Form 5x=(2x+1)^2

$5 x = {(2 x + 1)}^{2}$

Step 1

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

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

Step 2

Simplify $5 x - {(2 x + 1)}^{2}$ .

Simplify each term.

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

$5 x - ((2 x + 1) (2 x + 1)) = 0$

Expand $(2 x + 1) (2 x + 1)$ using the FOIL Method.

Apply the distributive property.

$5 x - (2 x (2 x + 1) + 1 (2 x + 1)) = 0$

Apply the distributive property.

$5 x - (2 x (2 x) + 2 x \cdot 1 + 1 (2 x + 1)) = 0$

Apply the distributive property.

$5 x - (2 x (2 x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1) = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 x - (2 \cdot 2 x \cdot x + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1) = 0$

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

Move $x$ .

$5 x - (2 \cdot 2 (x \cdot x) + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1) = 0$

Multiply $x$ by $x$ .

$5 x - (2 \cdot 2 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1) = 0$

Multiply $2$ by $2$ .

$5 x - (4 x^{2} + 2 x \cdot 1 + 1 (2 x) + 1 \cdot 1) = 0$

Multiply $2$ by $1$ .

$5 x - (4 x^{2} + 2 x + 1 (2 x) + 1 \cdot 1) = 0$

Multiply $2 x$ by $1$ .

$5 x - (4 x^{2} + 2 x + 2 x + 1 \cdot 1) = 0$

Multiply $1$ by $1$ .

$5 x - (4 x^{2} + 2 x + 2 x + 1) = 0$

Add $2 x$ and $2 x$ .

$5 x - (4 x^{2} + 4 x + 1) = 0$

Apply the distributive property.

$5 x - (4 x^{2}) - (4 x) - 1 \cdot 1 = 0$

Simplify.

Multiply $4$ by $- 1$ .

$5 x - 4 x^{2} - (4 x) - 1 \cdot 1 = 0$

Multiply $4$ by $- 1$ .

$5 x - 4 x^{2} - 4 x - 1 \cdot 1 = 0$

Multiply $- 1$ by $1$ .

$5 x - 4 x^{2} - 4 x - 1 = 0$

Subtract $4 x$ from $5 x$ .

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

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 $- 4 x^{2} + x - 1$ .

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

Step 5

Write in Standard Form 5x=(2x+1)^2

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