Algebra Examples

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

Step 1

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

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $(x + 7) (x - 7)$ .

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Step 1.1.1.1

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

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Step 1.1.1.1.1

Apply the distributive property.

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

Step 1.1.1.1.2

Apply the distributive property.

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

Step 1.1.1.1.3

Apply the distributive property.

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

Step 1.1.1.2

Simplify terms.

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Step 1.1.1.2.1

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

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Step 1.1.1.2.1.1

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

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

Step 1.1.1.2.1.2

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

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

Step 1.1.1.2.1.3

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

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

Step 1.1.1.2.2

Simplify each term.

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Step 1.1.1.2.2.1

Multiply $x$ by $x$ .

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

Step 1.1.1.2.2.2

Multiply $7$ by $- 7$ .

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

Step 1.2

Add $3$ to both sides of the equation.

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

Step 1.3

Add $- 49$ and $3$ .

$x^{2} - 46 = 0$

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.

$a = 1$ , $b = 0$ , $c = - 46$