Question

solve for x.
\\(x^2 + 16x - 17 = 0\\)
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
\\(x = \square\\)

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^2 + 16x - 17 = 0\). We look for two numbers that multiply to \(-17\) and add up to \(16\). The numbers are \(17\) and \(-1\) since \(17\times(-1)=-17\) and \(17 + (-1)=16\). So we can factor the equation as \((x + 17)(x - 1)=0\).

Step2: Solve for x

Set each factor equal to zero:

• For \(x + 17 = 0\), we subtract \(17\) from both sides: \(x=-17\).
• For \(x - 1 = 0\), we add \(1\) to both sides: \(x = 1\).

Answer:

\(1, -17\)