Find the Equation with Real Coefficients x=-4 , x=9

$x = - 4$ , $x = 9$

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 $0$ .

$(x - (- 4)) (x - 9) = 0$

Step 2

Simplify.

Expand $(x + 4) (x - 9)$ using the FOIL Method.

Apply the distributive property.

$x (x - 9) + 4 (x - 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 9 + 4 (x - 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 9 + 4 x + 4 \cdot - 9 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 9 + 4 x + 4 \cdot - 9 = 0$

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

$x^{2} - 9 \cdot x + 4 x + 4 \cdot - 9 = 0$

Multiply $4$ by $- 9$ .

$x^{2} - 9 x + 4 x - 36 = 0$

Add $- 9 x$ and $4 x$ .

$x^{2} - 5 x - 36 = 0$