Find the Equation Given the Roots x=-5 , x=7

$x = - 5$ , $x = 7$

Step 1

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(x - (- 5)) (x - 7) = 0$

Step 2

Simplify.

Expand $(x + 5) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) + 5 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 5 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 5 x + 5 \cdot - 7 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 7 + 5 x + 5 \cdot - 7 = 0$

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

$x^{2} - 7 \cdot x + 5 x + 5 \cdot - 7 = 0$

Multiply $5$ by $- 7$ .

$x^{2} - 7 x + 5 x - 35 = 0$

Add $- 7 x$ and $5 x$ .

$x^{2} - 2 x - 35 = 0$