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

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

Step 1

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

Simplify the left side.

Remove parentheses.

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

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

Subtract $x$ from both sides of the equation.

${(2 x - 1)}^{2} - x = 1$

Subtract $1$ from both sides of the equation.

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

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $- 1$ .

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

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

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

Combine the opposite terms in $4 x^{2} - 4 x + 1 - x - 1$ .

Subtract $1$ from $1$ .

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

Add $4 x^{2} - 4 x - x$ and $0$ .

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

Subtract $x$ from $- 4 x$ .

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

Step 2

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

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

Step 3

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

$a = 4$ , $b = - 5$ , $c = 0$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.