Find the Quadratic Equation 9 , -6

$9$ , $- 6$

Step 1

$x = 9$ and $x = - 6$ are the two real distinct solutions for the quadratic equation, which means that $x - 9$ and $x + 6$ are the factors of the quadratic equation.

$(x - 9) (x + 6) = 0$

Step 2

Expand $(x - 9) (x + 6)$ using the FOIL Method.

Apply the distributive property.

$x (x + 6) - 9 (x + 6) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 6 - 9 (x + 6) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 6 - 9 x - 9 \cdot 6 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $6$ to the left of $x$ .

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

Multiply $- 9$ by $6$ .

$x^{2} + 6 x - 9 x - 54 = 0$

Subtract $9 x$ from $6 x$ .

$x^{2} - 3 x - 54 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${9, - 6}$ is $y = x^{2} - 3 x - 54$ .

$y = x^{2} - 3 x - 54$

Step 5

Find the Quadratic Equation 9 , -6

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