Find the Quadratic Equation 14 , 8

$14$ , $8$

Step 1

$x = 14$ and $x = 8$ are the two real distinct solutions for the quadratic equation, which means that $x - 14$ and $x - 8$ are the factors of the quadratic equation.

$(x - 14) (x - 8) = 0$

Step 2

Expand $(x - 14) (x - 8)$ using the FOIL Method.

Apply the distributive property.

$x (x - 8) - 14 (x - 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 8 - 14 (x - 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 8 - 14 x - 14 \cdot - 8 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 8 - 14 x - 14 \cdot - 8 = 0$

Move $- 8$ to the left of $x$ .

$x^{2} - 8 \cdot x - 14 x - 14 \cdot - 8 = 0$

Multiply $- 14$ by $- 8$ .

$x^{2} - 8 x - 14 x + 112 = 0$

Subtract $14 x$ from $- 8 x$ .

$x^{2} - 22 x + 112 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${14, 8}$ is $y = x^{2} - 22 x + 112$ .

$y = x^{2} - 22 x + 112$

Step 5

Find the Quadratic Equation 14 , 8

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