Algebra Examples

$(- 7, 7)$

Step 1

$x = - 7$ and $x = 7$ are the two real distinct solutions for the quadratic equation, which means that $x + 7$ and $x - 7$ are the factors of the quadratic equation.

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

Multiply $7$ by $- 7$ .

$x^{2} - 49 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 7, 7}$ is $y = x^{2} - 49$ .

$y = x^{2} - 49$

Step 5