Algebra Examples

$- x^{2} + 4 = {(3 x - 1)}^{2}$

Step 1

Subtract ${(3 x - 1)}^{2}$ from both sides of the equation.

$- x^{2} + 4 - {(3 x - 1)}^{2} = 0$

Step 2

Simplify $- x^{2} + 4 - {(3 x - 1)}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(3 x - 1)}^{2}$ as $(3 x - 1) (3 x - 1)$ .

$- x^{2} + 4 - ((3 x - 1) (3 x - 1)) = 0$

Step 2.1.2

Expand $(3 x - 1) (3 x - 1)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$- x^{2} + 4 - (3 x (3 x - 1) - 1 (3 x - 1)) = 0$

Step 2.1.2.2

Apply the distributive property.

$- x^{2} + 4 - (3 x (3 x) + 3 x \cdot - 1 - 1 (3 x - 1)) = 0$

Step 2.1.2.3

Apply the distributive property.

$- x^{2} + 4 - (3 x (3 x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1) = 0$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Rewrite using the commutative property of multiplication.

$- x^{2} + 4 - (3 \cdot 3 x \cdot x + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1) = 0$

Step 2.1.3.1.2

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

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Step 2.1.3.1.2.1

Move $x$ .

$- x^{2} + 4 - (3 \cdot 3 (x \cdot x) + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1) = 0$

Step 2.1.3.1.2.2

Multiply $x$ by $x$ .

$- x^{2} + 4 - (3 \cdot 3 x^{2} + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1) = 0$

Step 2.1.3.1.3

Multiply $3$ by $3$ .

$- x^{2} + 4 - (9 x^{2} + 3 x \cdot - 1 - 1 (3 x) - 1 \cdot - 1) = 0$

Step 2.1.3.1.4

Multiply $- 1$ by $3$ .

$- x^{2} + 4 - (9 x^{2} - 3 x - 1 (3 x) - 1 \cdot - 1) = 0$

Step 2.1.3.1.5

Multiply $3$ by $- 1$ .

$- x^{2} + 4 - (9 x^{2} - 3 x - 3 x - 1 \cdot - 1) = 0$

Step 2.1.3.1.6

Multiply $- 1$ by $- 1$ .

$- x^{2} + 4 - (9 x^{2} - 3 x - 3 x + 1) = 0$

Step 2.1.3.2

Subtract $3 x$ from $- 3 x$ .

$- x^{2} + 4 - (9 x^{2} - 6 x + 1) = 0$

Step 2.1.4

Apply the distributive property.

$- x^{2} + 4 - (9 x^{2}) - (- 6 x) - 1 \cdot 1 = 0$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $9$ by $- 1$ .

$- x^{2} + 4 - 9 x^{2} - (- 6 x) - 1 \cdot 1 = 0$

Step 2.1.5.2

Multiply $- 6$ by $- 1$ .

$- x^{2} + 4 - 9 x^{2} + 6 x - 1 \cdot 1 = 0$

Step 2.1.5.3

Multiply $- 1$ by $1$ .

$- x^{2} + 4 - 9 x^{2} + 6 x - 1 = 0$

Step 2.2

Subtract $9 x^{2}$ from $- x^{2}$ .

$- 10 x^{2} + 4 + 6 x - 1 = 0$

Step 2.3

Subtract $1$ from $4$ .

$- 10 x^{2} + 6 x + 3 = 0$

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 $- 10 x^{2} + 6 x + 3$ .

$- 10 x^{2} + 6 x + 3 = 0$

Step 5