Rewrite the quadratic equation x² - 8x + 13 = 0 to the form (x - a)² = b, where a and b are integers, to determine the a and b values.

Solution:

Given quadratic equation is x² - 8x + 13 = 0

To bring it to the form (x - a)² = b, we use the technique of completing the square.

Rewrite the equation x² - 8x + 13 = 0

This is of the standard form ax² +bx + c = 0

For completing the square, we follow these steps:

• Take the constant to the other side
• Find half of b and square it.
• Add it to both sides and complete the square using the known square algebraic identity.

Step 1: x² - 8x = -13

Step 2: x² - 8x + 4² = -13 + 4²

Step 3: (x-4)² = -13 + 16 [using the algebraic identity [(a - b)² = a² - 2ab + b² ]

(x - 4)² = 3

Comparing the above equation with (x - a)² = b

Gives a = 4, b = 3

Rewrite the quadratic equation x² - 8x + 13 = 0 to the form (x - a)² = b, where a and b are integers, to determine the a and b values.

Summary:

The quadratic equation x² - 8x + 13 = 0 to the form (x - a)² = b, where a and b are integers, are determined as a = 4 and b = 3.