Algebra Examples

$2 x - 3 = 2 {(x - 1)}^{2}$

Step 1

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

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Step 1.1

Simplify the right side.

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Step 1.1.1

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

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Step 1.1.1.1

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

$2 x - 3 = 2 ((x - 1) (x - 1))$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Apply the distributive property.

$2 x - 3 = 2 (x (x - 1) - 1 (x - 1))$

Step 1.1.1.2.2

Apply the distributive property.

$2 x - 3 = 2 (x \cdot x + x \cdot - 1 - 1 (x - 1))$

Step 1.1.1.2.3

Apply the distributive property.

$2 x - 3 = 2 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Step 1.1.1.3

Simplify and combine like terms.

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Step 1.1.1.3.1

Simplify each term.

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Step 1.1.1.3.1.1

Multiply $x$ by $x$ .

$2 x - 3 = 2 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Step 1.1.1.3.1.2

Move $- 1$ to the left of $x$ .

$2 x - 3 = 2 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1)$

Step 1.1.1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$2 x - 3 = 2 (x^{2} - x - 1 x - 1 \cdot - 1)$

Step 1.1.1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$2 x - 3 = 2 (x^{2} - x - x - 1 \cdot - 1)$

Step 1.1.1.3.1.5

Multiply $- 1$ by $- 1$ .

$2 x - 3 = 2 (x^{2} - x - x + 1)$

Step 1.1.1.3.2

Subtract $x$ from $- x$ .

$2 x - 3 = 2 (x^{2} - 2 x + 1)$

Step 1.1.1.4

Apply the distributive property.

$2 x - 3 = 2 x^{2} + 2 (- 2 x) + 2 \cdot 1$

Step 1.1.1.5

Simplify.

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Step 1.1.1.5.1

Multiply $- 2$ by $2$ .

$2 x - 3 = 2 x^{2} - 4 x + 2 \cdot 1$

Step 1.1.1.5.2

Multiply $2$ by $1$ .

$2 x - 3 = 2 x^{2} - 4 x + 2$

Step 1.2

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

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Step 1.2.1

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

$2 x - 3 - 2 x^{2} = - 4 x + 2$

Step 1.2.2

Add $4 x$ to both sides of the equation.

$2 x - 3 - 2 x^{2} + 4 x = 2$

Step 1.2.3

Subtract $2$ from both sides of the equation.

$2 x - 3 - 2 x^{2} + 4 x - 2 = 0$

Step 1.3

Simplify $2 x - 3 - 2 x^{2} + 4 x - 2$ .

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Step 1.3.1

Add $2 x$ and $4 x$ .

$6 x - 3 - 2 x^{2} - 2 = 0$

Step 1.3.2

Subtract $2$ from $- 3$ .

$6 x - 2 x^{2} - 5 = 0$

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.

$a = - 2$ , $b = 6$ , $c = - 5$