Write in Standard Form -x^2+5=(4x-1)^2

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

Step 1

Subtract ${(4 x - 1)}^{2}$ from both sides of the equation.

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

Step 2

Simplify $- x^{2} + 5 - {(4 x - 1)}^{2}$ .

Simplify each term.

Rewrite ${(4 x - 1)}^{2}$ as $(4 x - 1) (4 x - 1)$ .

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

Expand $(4 x - 1) (4 x - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$- x^{2} + 5 - (16 x^{2} + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1) = 0$

Multiply $- 1$ by $4$ .

$- x^{2} + 5 - (16 x^{2} - 4 x - 1 (4 x) - 1 \cdot - 1) = 0$

Multiply $4$ by $- 1$ .

$- x^{2} + 5 - (16 x^{2} - 4 x - 4 x - 1 \cdot - 1) = 0$

Multiply $- 1$ by $- 1$ .

$- x^{2} + 5 - (16 x^{2} - 4 x - 4 x + 1) = 0$

Subtract $4 x$ from $- 4 x$ .

$- x^{2} + 5 - (16 x^{2} - 8 x + 1) = 0$

Apply the distributive property.

$- x^{2} + 5 - (16 x^{2}) - (- 8 x) - 1 \cdot 1 = 0$

Simplify.

Multiply $16$ by $- 1$ .

$- x^{2} + 5 - 16 x^{2} - (- 8 x) - 1 \cdot 1 = 0$

Multiply $- 8$ by $- 1$ .

$- x^{2} + 5 - 16 x^{2} + 8 x - 1 \cdot 1 = 0$

Multiply $- 1$ by $1$ .

$- x^{2} + 5 - 16 x^{2} + 8 x - 1 = 0$

Subtract $16 x^{2}$ from $- x^{2}$ .

$- 17 x^{2} + 5 + 8 x - 1 = 0$

Subtract $1$ from $5$ .

$- 17 x^{2} + 8 x + 4 = 0$

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 $- 17 x^{2} + 8 x + 4$ .

$- 17 x^{2} + 8 x + 4 = 0$

Step 5

Write in Standard Form -x^2+5=(4x-1)^2

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