Find the Quadratic Equation 5 , 9

$5$ , $9$

Step 1

$x = 5$ and $x = 9$ are the two real distinct solutions for the quadratic equation, which means that $x - 5$ and $x - 9$ are the factors of the quadratic equation.

$(x - 5) (x - 9) = 0$

Step 2

Expand $(x - 5) (x - 9)$ using the FOIL Method.

Apply the distributive property.

$x (x - 9) - 5 (x - 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 9 - 5 (x - 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 9 - 5 x - 5 \cdot - 9 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 9 - 5 x - 5 \cdot - 9 = 0$

Move $- 9$ to the left of $x$ .

$x^{2} - 9 \cdot x - 5 x - 5 \cdot - 9 = 0$

Multiply $- 5$ by $- 9$ .

$x^{2} - 9 x - 5 x + 45 = 0$

Subtract $5 x$ from $- 9 x$ .

$x^{2} - 14 x + 45 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${5, 9}$ is $y = x^{2} - 14 x + 45$ .

$y = x^{2} - 14 x + 45$

Step 5

Find the Quadratic Equation 5 , 9

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