Solve the equation 0=x2−12x+20 algebraically using any method. Provide the smaller-valued solution in the first response field and the larger-valued solution in the second response field.

Answer 1

To solve the equation \( 0 = x^2 - 12x + 20 \), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

where \( a = 1 \), \( b = -12 \), and \( c = 20 \).

First, we calculate the discriminant:

\[ b^2 - 4ac = (-12)^2 - 4 \times 1 \times 20 = 144 - 80 = 64 \]

Now applying the quadratic formula:

\[ x = \frac{12 \pm \sqrt{64}}{2 \times 1} = \frac{12 \pm 8}{2} \]

This gives us two solutions:

1. \( x = \frac{12 + 8}{2} = \frac{20}{2} = 10 \)
2. \( x = \frac{12 - 8}{2} = \frac{4}{2} = 2 \)

The smaller-valued solution is:

2

The larger-valued solution is:

10