Question

solve for all values of x by factoring.
$x^2 + 2x - 80 = 0$
answer attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-80\) and add up to \(2\). Let's list the factor pairs of \(80\): \((1,80)\), \((2,40)\), \((4,20)\), \((5,16)\), \((8,10)\). Among these, \(10\) and \(-8\) work because \(10\times(-8)= -80\) and \(10 + (-8)=2\).

Step2: Factor the quadratic

Using the numbers from Step 1, we can factor \(x^{2}+2x - 80\) as \((x + 10)(x - 8)=0\).

Step3: Solve for \(x\)

Set each factor equal to zero:

• For \(x + 10 = 0\), we get \(x=-10\).
• For \(x - 8 = 0\), we get \(x = 8\).

Answer:

\(x=-10\) or \(x = 8\)