Question

1. $x^2 - 18x = -17$
2. $x^2 + 12x = -8$

Explanation:

Step1: Rearrange the equation

We start with the equation \(x^{2}-18x = - 17\). Add 17 to both sides to get it in standard quadratic form \(ax^{2}+bx + c=0\). So we have \(x^{2}-18x + 17=0\).

Step2: Factor the quadratic

We need to find two numbers that multiply to \(17\) (the constant term) and add up to \(- 18\) (the coefficient of \(x\)). The numbers are \(-1\) and \(-17\) because \((-1)\times(-17)=17\) and \((-1)+(-17)=-18\). So we can factor the quadratic as \((x - 1)(x - 17)=0\).

Step3: Solve for x

Set each factor equal to zero:

• For \(x - 1=0\), we get \(x = 1\).
• For \(x - 17=0\), we get \(x = 17\).

Answer:

The solutions are \(x = 1\) and \(x = 17\)