Question

values of x by factoring.

x² + 2x - 80 = 0

attempt 1 out of 2

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -80 and add up to 2. The numbers are 10 and -8 since \(10\times(-8)= - 80\) and \(10+( - 8)=2\).

Step2: Factor the quadratic

Rewrite the middle term using these two numbers: \(x^{2}+10x - 8x-80 = 0\). Then factor by grouping: \(x(x + 10)-8(x + 10)=0\), which gives \((x + 10)(x - 8)=0\).

Step3: Solve for x

Set each factor equal to zero: \(x+10 = 0\) or \(x - 8=0\). Solving these gives \(x=-10\) or \(x = 8\).

Answer:

The solutions are \(x=-10\) and \(x = 8\)