Write in Standard Form 4x+7=(x-5)^2

$4 x + 7 = {(x - 5)}^{2}$

Step 1

Subtract ${(x - 5)}^{2}$ from both sides of the equation.

$4 x + 7 - {(x - 5)}^{2} = 0$

Step 2

Simplify $4 x + 7 - {(x - 5)}^{2}$ .

Simplify each term.

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$4 x + 7 - ((x - 5) (x - 5)) = 0$

Expand $(x - 5) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$4 x + 7 - (x (x - 5) - 5 (x - 5)) = 0$

Apply the distributive property.

$4 x + 7 - (x \cdot x + x \cdot - 5 - 5 (x - 5)) = 0$

Apply the distributive property.

$4 x + 7 - (x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5) = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$4 x + 7 - (x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5) = 0$

Move $- 5$ to the left of $x$ .

$4 x + 7 - (x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5) = 0$

Multiply $- 5$ by $- 5$ .

$4 x + 7 - (x^{2} - 5 x - 5 x + 25) = 0$

Subtract $5 x$ from $- 5 x$ .

$4 x + 7 - (x^{2} - 10 x + 25) = 0$

Apply the distributive property.

$4 x + 7 - x^{2} - (- 10 x) - 1 \cdot 25 = 0$

Simplify.

Multiply $- 10$ by $- 1$ .

$4 x + 7 - x^{2} + 10 x - 1 \cdot 25 = 0$

Multiply $- 1$ by $25$ .

$4 x + 7 - x^{2} + 10 x - 25 = 0$

Add $4 x$ and $10 x$ .

$14 x + 7 - x^{2} - 25 = 0$

Subtract $25$ from $7$ .

$14 x - x^{2} - 18 = 0$

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 $14 x$ and $- x^{2}$ .

$- x^{2} + 14 x - 18 = 0$

Step 5