Find a,b,c 5x=(2x+1)^2

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

Move all terms to the left side of the equation and simplify.

Simplify the right side.

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $1$ .

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

Multiply $2 x$ by $1$ .

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

Multiply $1$ by $1$ .

$5 x = 4 x^{2} + 2 x + 2 x + 1$

Add $2 x$ and $2 x$ .

$5 x = 4 x^{2} + 4 x + 1$

Move all the expressions to the left side of the equation.

Subtract $4 x^{2}$ from both sides of the equation.

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

Subtract $4 x$ from both sides of the equation.

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

Subtract $1$ from both sides of the equation.

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

Subtract $4 x$ from $5 x$ .

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

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = - 4$ , $b = 1$ , $c = - 1$