To factor the quadratic equation, use the quadratic formula.
To a quadratic equation ax² + bx + c = 0, the quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Given the quadratic equation x² + 3x - 18 = 0, the coefficients are:
a = 1
b = 3
c = -18
Substituting the coefficients and solving the equation:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{3^2-4*1*(-18)}}{2*1} \\ x=\frac{-3\pm\sqrt{9+72}}{2} \\ x=\frac{-3\pm\sqrt{81}}{2} \\ x=\frac{-3\pm9}{2} \\ x_1=\frac{-3-9}{2}=-\frac{12}{2}=-6 \\ x_2=\frac{-3+9}{2}=\frac{6}{2}=3 \end{gathered}[/tex]
So, the roots are: -6 and 3.
If a quadratic equation has roots x₁ and x₂, then the equation in the factored form is (x - x₁)(x - x₂).
So,
x² + 3x - 18 = (x - 3)(x + 6).
Answer: (x - 3)(x + 6).
