Find the Quadratic Equation -6 , 6

$- 6$ , $6$

$x = - 6$ and $x = 6$ are the two real distinct solutions for the quadratic equation, which means that $x + 6$ and $x - 6$ are the factors of the quadratic equation.

$(x + 6) (x - 6) = 0$

Expand $(x + 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$x (x - 6) + 6 (x - 6) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 6 + 6 (x - 6) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 6 + 6 x + 6 \cdot - 6 = 0$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot - 6 + 6 x + 6 \cdot - 6$ .

Reorder the factors in the terms $x \cdot - 6$ and $6 x$ .

$x \cdot x - 6 x + 6 x + 6 \cdot - 6 = 0$

Add $- 6 x$ and $6 x$ .

$x \cdot x + 0 + 6 \cdot - 6 = 0$

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

$x \cdot x + 6 \cdot - 6 = 0$

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $6$ by $- 6$ .

$x^{2} - 36 = 0$

The standard quadratic equation using the given set of solutions ${- 6, 6}$ is $y = x^{2} - 36$ .

$y = x^{2} - 36$

Find the Quadratic Equation -6 , 6

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