Find the Quadratic Equation 5 , -8

$5$ , $- 8$

Step 1

$x = 5$ and $x = - 8$ are the two real distinct solutions for the quadratic equation, which means that $x - 5$ and $x + 8$ are the factors of the quadratic equation.

$(x - 5) (x + 8) = 0$

Step 2

Expand $(x - 5) (x + 8)$ using the FOIL Method.

Apply the distributive property.

$x (x + 8) - 5 (x + 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 - 5 (x + 8) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 8 - 5 x - 5 \cdot 8 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 8 - 5 x - 5 \cdot 8 = 0$

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

$x^{2} + 8 \cdot x - 5 x - 5 \cdot 8 = 0$

Multiply $- 5$ by $8$ .

$x^{2} + 8 x - 5 x - 40 = 0$

Subtract $5 x$ from $8 x$ .

$x^{2} + 3 x - 40 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${5, - 8}$ is $y = x^{2} + 3 x - 40$ .

$y = x^{2} + 3 x - 40$

Step 5

Find the Quadratic Equation 5 , -8

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