Algebra Examples

$(x + 7) (x - 7) = - 3 x$

Step 1

Add $3 x$ to both sides of the equation.

$(x + 7) (x - 7) + 3 x = 0$

Step 2

Simplify each term.

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Step 2.1

Expand $(x + 7) (x - 7)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$x (x - 7) + 7 (x - 7) + 3 x = 0$

Step 2.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 7 (x - 7) + 3 x = 0$

Step 2.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 7 x + 7 \cdot - 7 + 3 x = 0$

Step 2.2

Combine the opposite terms in $x \cdot x + x \cdot - 7 + 7 x + 7 \cdot - 7$ .

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Step 2.2.1

Reorder the factors in the terms $x \cdot - 7$ and $7 x$ .

$x \cdot x - 7 x + 7 x + 7 \cdot - 7 + 3 x = 0$

Step 2.2.2

Add $- 7 x$ and $7 x$ .

$x \cdot x + 0 + 7 \cdot - 7 + 3 x = 0$

Step 2.2.3

Add $x \cdot x$ and $0$ .

$x \cdot x + 7 \cdot - 7 + 3 x = 0$

Step 2.3

Simplify each term.

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Step 2.3.1

Multiply $x$ by $x$ .

$x^{2} + 7 \cdot - 7 + 3 x = 0$

Step 2.3.2

Multiply $7$ by $- 7$ .

$x^{2} - 49 + 3 x = 0$

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

Move $- 49$ .

$x^{2} + 3 x - 49 = 0$

Step 5