Find the Quadratic Equation (-6,-7)

$(- 6, - 7)$

Step 1

$x = - 6$ and $x = - 7$ are the two real distinct solutions for the quadratic equation, which means that $x + 6$ and $x + 7$ are the factors of the quadratic equation.

$(x + 6) (x + 7) = 0$

Step 2

Expand $(x + 6) (x + 7)$ using the FOIL Method.

Apply the distributive property.

$x (x + 7) + 6 (x + 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 7 + 6 (x + 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 7 + 6 x + 6 \cdot 7 = 0$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 7 + 6 x + 6 \cdot 7 = 0$

Move $7$ to the left of $x$ .

$x^{2} + 7 \cdot x + 6 x + 6 \cdot 7 = 0$

Multiply $6$ by $7$ .

$x^{2} + 7 x + 6 x + 42 = 0$

Add $7 x$ and $6 x$ .

$x^{2} + 13 x + 42 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${- 6, - 7}$ is $y = x^{2} + 13 x + 42$ .

$y = x^{2} + 13 x + 42$

Step 5

Find the Quadratic Equation (-6,-7)

Related Questions

Support LCMGCF.com by disabling your adblocker.