Question

solve the equation by factoring: ( x^2 + 11x + 30 = 0 )
a ( x = -5, x = -6 )
b ( x = 5, x = 6 )
c ( x = -5, x = 6 )
d ( x = 5, x = -6 )

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^{2}+11x + 30=0\). We look for two numbers that multiply to \(30\) and add up to \(11\). The numbers \(5\) and \(6\) satisfy this because \(5\times6 = 30\) and \(5 + 6=11\). So we can factor the quadratic as \((x + 5)(x+6)=0\).

Step2: Solve for \(x\)

Using the zero - product property, if \((x + 5)(x + 6)=0\), then either \(x+5 = 0\) or \(x + 6=0\).

• If \(x+5=0\), then \(x=-5\) (by subtracting \(5\) from both sides of the equation).
• If \(x + 6=0\), then \(x=-6\) (by subtracting \(6\) from both sides of the equation).

Answer:

A. \(x=-5,x = - 6\)