Question

1. ( x^2 - 12x = -8 )

Explanation:

Step1: Rewrite the equation in standard form

Add 8 to both sides of the equation \(x^{2}-12x=-8\) to get \(x^{2}-12x + 8=0\).

Step2: Use the quadratic formula

For a quadratic equation \(ax^{2}+bx + c = 0\) (\(a
eq0\)), the quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Here, \(a = 1\), \(b=-12\), and \(c = 8\).
First, calculate the discriminant \(\Delta=b^{2}-4ac=(-12)^{2}-4\times1\times8=144 - 32 = 112\).
Then, find the roots:
\(x=\frac{-(-12)\pm\sqrt{112}}{2\times1}=\frac{12\pm4\sqrt{7}}{2}=6\pm2\sqrt{7}\)

Answer:

\(x = 6 + 2\sqrt{7}\) or \(x = 6 - 2\sqrt{7}\)